Partnership for AiR Transportation Noise and Emissions ReductionAn FAA/NASA/Transport Canada-sponsored Center of Excellence

Uncertainty Quantification of Aviation Fuel Burn Performance

A PARTNER Project 48 report

prepared bySergio Amaral, Elena de la Rosa Blanco, Douglas Allaire, Karen E. Willcox

September 2016

REPORT NO. PARTNER-COE-2016-003

Uncertainty Quantification of Aviation Fuel Burn Performance

A PARTNER Project 48 Report

Sergio Amaral, Elena de la Rosa Blanco, Douglas Allaire, Karen E. Willcox

PARTNER-COE-2016-003 September 2016

This work was funded by the US Federal Aviation Administration Office of Environment and Energy. The project was managed by James Skalecky of the FAA.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the FAA, NASA, Transport Canada, the U.S. Department of Defense, or the U.S. Environmental Protection Agency

The Partnership for AiR Transportation Noise and Emissions Reduction — PARTNER — is a cooperative aviation research organization, and an FAA/NASA/Transport Canada-sponsored Center of Excellence. PARTNER fosters breakthrough technological, operational, policy, and workforce advances for the betterment of mobility, economy, national security, and the environment. The organization's operational headquarters is at the Massachusetts Institute of Technology.

The Partnership for AiR Transportation Noise and Emissions Reduction Massachusetts Institute of Technology, 77 Massachusetts Avenue, 33-240

Cambridge, MA 02139 USA partner.aero

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UncertaintyQuantificationofAviationFuelBurnPerformance

Author:

SergioAmaral

ProjectSupervisors:

ElenadelaRosaBlanco

DouglasAllaire

KarenE.Willcox

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Summary

Estimating future aircraft fuel burn performance is essentialwhen setting aviation standardsandefficiencygoalsforfuturecommercialaviation.Changesinfuelefficiencymayresultfromaviation technology enhancements and/or adjustments in aviation operations. In order tosupport effective decision-making, it is important that fuel burn estimates come with anassessment of the associated uncertainties. This report presents a quantitative approach toevaluatingtheuncertaintyofaircraftfuelburnperformanceanddeterminingwhichfactors inaircraft technologies or design operations cause the greatest variation in the fuel burnperformance. The report investigates varying aircraft configurations using a conventionalBoeing737-800aircraftandanunconventionalconfigurationMITD8(DoubleBubble)aircraft.We also investigate varying aviation technologies with the D8 configuration using currenttechnologiesandadvancedtechnologies.

Aircraft flight performance in relation to aircraft technologies, design operations, and theirinteractions is modeled using the software tool Transport Aviation Systems Optimization(TASOpt). The software TASOpt allows users to evaluate future aircraft with potentiallyunconventional airframe, aerodynamic, engine, or operational parameters. The aircraftdesignedinTASOptarethenimportedintotheFAAsoftwarepackageAviationEnvironmentalDesignToolVersion2a(AEDT2a)toevaluatetheaircraftsfuelburnperformance.Thecouplingof TASOpt and AEDT into a system-level analysis tool allows one to model theinterdependenciesbetweenaircraft technologyanddesignoperationof conventional aircraftaswellasunconventionalaircraft.

The coupling of TASOpt and AEDT into a system-level analysis tool requires compilingapproximatelyonehundredAEDTaircraftperformanceparametersandcoefficientsusing theTASOptaircraftflightperformanceoutput.TheconnectionbetweenTASOptandAEDTisshowntobeaccurateinregardstototalfuelburnperformancetowithin5%relativeuncertaintyoversimilarflightscenarios,whereuncertaintyreferstothedifferencebetweenTASOptandAEDTestimations of the fuel burn. The discrepancy between TASOpt and AEDT fuel burnperformance is typicallyobservednear thedepartureandarrival segments. Inparticular, theTASOpt and AEDT fuel burn performance in the approach segment, from cruise to airportarrival, has an approximately 15% relative uncertainty due to the varying methodologiesbetweenTASOptandAEDT.TheTASOpttoAEDTfuelburnperformanceforcruisevarieswiththe worst case being approximately 3% relative uncertainty due to the differences in initialtakeoffweight.

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For the Boeing 737-800 fuel burn performance, which is evaluated using the fuel energyconsumptionperpayload range (PFEI), has the largest expectationandvarianceof the threeaircraft configurations. The 737-800’s PFEI variation is attributed to two main sources;uncertainties in the aircraft’s design cruising altitude and the aircraft’swing cap yield stresstechnologicalvariable.TheD8withstandardtechnologyhasa lowerexpectedPFEImeanandvariance than the Boeing 737-800. That is, for the scenarios studied, the unconventional D8aircraft configuration reduces the variability in fuel burnperformance. TheD8with standardtechnology PFEI variation is susceptible to multiple aircraft technology uncertainties andoperational uncertainties, whereas the Boeing 737-800 has only two important factorscontributing to variability in its fuel burn performance. Finally, the D8 with advancedtechnology has the lowest PFEI mean and variance of the three aircraft configurations.Furthermore, the D8 with advanced technology has only two significant contributinguncertainties to PFEI uncertainty; turbine inlet gas temperature and aircraft design Machnumber. These results indicate that large variations in aircraft configuration and technologysubstantiallymodifytheresearchprioritizationefforts.

The report also presents a new approach to evaluating the system-level uncertaintyquantification using a decomposition-based methodology. The decomposition-baseduncertainty quantification approachhasmultiple benefits in comparison to a standard all-at-once system-level uncertainty quantification approach. The decomposition-based uncertaintyquantificationapproachbreaks the system-level analysis intomanageable componentswhichcan be individually analyzed by the respective component experts using local resources.However, the decomposition-based uncertainty quantification approach is challenging whentheinterfacebetweentwocomponentsinasystemcontainsalargenumberofvariablesasthisproblemdoes. This report presentsour current findingsondecomposition-baseduncertaintyquantification of a large scale system. The results show great potential for decomposition-baseduncertaintyquantification.But,furtherresearchisrequiredtoaccuratelyandrigorouslyperformthedecomposition-baseduncertaintyquantificationonlarge-scalesystems.

The report contains a step-by-step procedure and necessary scripts for initializing TASOpt,AEDT, and integrating the twomodules. In this reportwe have addressed the following keyissues: analyzing non-conventional and other unrepresented aircraft in AEDT, assessing howuncertainties in aircraft technologies and design operations impact fuel burn performance,assessing how fuel burn performance is impacted by aircraft configurations and aviationtechnology enhancements, and demonstrating the decomposition-based uncertaintyquantificationonalarge-scaleapplicationproblem.

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TableofContentsSummary_____________________________________________________________________1

ListofFigures_________________________________________________________________5

ListofTables__________________________________________________________________7

Nomenclature_________________________________________________________________8

Introduction_________________________________________________________________10

Motivation_______________________________________________________________________10

Methodology_____________________________________________________________________11

System-LevelUncertaintyQuantification_______________________________________________12

Decomposition-BasedUncertaintyQuantification _______________________________________15

TASOpt _____________________________________________________________________17

SourceCodeModifications__________________________________________________________17

AircraftConfiguration______________________________________________________________19

TASOptInputParameters___________________________________________________________20

AEDT_______________________________________________________________________27

AEDTFleetDatabase_______________________________________________________________27

FlightTrajectory___________________________________________________________________28

AEDTRunStudy___________________________________________________________________30

TASOpt-AEDTConnection ______________________________________________________32

DataFormat______________________________________________________________________32

Transformation ___________________________________________________________________34

Validation________________________________________________________________________56

System-LevelMCSUncertaintyQuantification______________________________________59

B738StandardTechnology__________________________________________________________60

D8StandardTechnology____________________________________________________________64

D8AdvancedTechnology ___________________________________________________________67

Decomposition-BasedUncertaintyQuantification___________________________________70

TASOpt-AEDTInterfaceChallenge ____________________________________________________70

DimensionReduction ______________________________________________________________71

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ProposalDistribution_______________________________________________________________72

Proposal-to-TargetTransformation ___________________________________________________73

UncertaintyAnalysis _______________________________________________________________74

Conclusion___________________________________________________________________76

References __________________________________________________________________78

GlobalSensitivityAnalysis______________________________________________________79

TASOptInputFiles(*.tas) ______________________________________________________80

AEDTSQLFleetDatabaseImport(*.sql)___________________________________________82

SQLScripttoDuplicateOperations_______________________________________________87

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ListofFiguresFigure1:System-levelUQofthetoolsetconsistsofquantifyinghowuncertaintyinaircrafttechnologyanddesignoperationsimpactstheuncertaintyintheoutputsofinterest(e.g.,fuelburn).............................................................................................................................................11Figure2:System-leveluncertaintyanalysisusingthesampling-basedtechnique(e.g.,MCS)....13Figure3:Uniformsampling(Left:Pseudo-Random)(Right:Quasi-Random)...............................14Figure4:Globalsensitivityanalysisvariancedecomposition(Allaire,2009)...............................15Figure5:Theproposedmethodofmulticomponentuncertaintyanalysisdecomposestheproblemintomanageablecomponents;similartodecomposition-basedapproachesusedinmultidisciplinaryanalysisandoptimization,andsynthesizethesystemuncertaintyanalysiswithoutneedingtoevaluatethesysteminitsentirety...............................................................16Figure6:Illustrationoftheproposedmethodfordecomposition-basedglobalsensitivityanalysis.........................................................................................................................................16Figure7:Boeing737-800andMITD8airframeconfigurations[6]..............................................19Figure8:Historicaltrendsforenginemetaltemperaturecapacity(Kyprianidis,2011)..............20Figure9:Historicaltrendsforturbineentrytotaltemperature(Kyprianidis,2011)....................22Figure10:Historicaltrendsforengineoverallpressureratio(Gunston,1998)...........................23Figure11:Startingfromtheoptimalaircraftconfiguration(blueaircraft)weincorporateuncertaintiestocharacterizethelackofknowledgeinaircrafttechnologyanddesignoperations.Thenew(uncertainrealization)aircraftisresizedtomeetthedesiredfirstmissionflightspecification(redaircraft).The(red)aircraftisthenflownovermultiplemissionscenariostoextratheaircraftflightperformance.ThisinturnisthenimportedintotheAEDTSQLFLEETDatabasetocreateanequivalentaircraftinAEDT......................................................................26Figure12:AEDTUQ20greatcircleflighttrajectories..................................................................30Figure13:ValidationtrajectoryforTASOpt&AEDT....................................................................56Figure14:D8withstandardtechnologyBOS-ATLflightsensorpathaltitudeandtrueairspeed.......................................................................................................................................................57Figure15:D8withstandardtechnologyAEDTvsTASOptBOS-ATLFuelBurnandNetCorrectThrustResults...............................................................................................................................58Figure16:B738totalfuelenergyperpayloadrangedistribution...............................................61Figure17:B738fuelenergyperpayloadrangesensitivityindex.................................................61Figure18:B738MCSresultsofPFEIagainsttheaircrafttechnologyparameters.......................62Figure19:WingorTailSection(Drela,SimultaneousOptimizationoftheAirframe,Powerplant,andOperationofTransportAircraft.,2010)................................................................................63Figure20:B738AircraftEmptyWeightSensitivityAnalysis.........................................................63Figure21:GlobalsensitivityindexforTC1andCf1........................................................................63Figure22:D8StandardTechnologyPFEIdistribution..................................................................64

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Figure23:D8StandardTechnologyPFEIsensitivityanalysis.......................................................64Figure24:D8StandardTechnologyMCSresultsofPFEIagainsttheaircrafttechnologyparameters...................................................................................................................................65Figure25:D8StandardTechnologyAircraftEmptyWeightSensitivityAnalysis..........................66Figure26:D8StandardTechnologyGlobalsensitivityindexforCTC,1andCf1..............................66Figure27:D8StandardTechnologyGlobalsensitivityindexforC0,CRandC2,CR.......................66Figure28:D8AdvancedTechnologyPFEIdistribution.................................................................67Figure29:D8AdvancedTechnologyPFEIsensitivityanalysis......................................................67Figure30:D8AdvancedtechnologyMCSresultsofPFEIagainsttheaircrafttechnologyparameters...................................................................................................................................68Figure31:D8advancedtechnologyGlobalsensitivityindexforCTC,1andCf1..........................69Figure32:D8advancedtechnologyGlobalsensitivityindexforC0,CRandC2,CR......................69Figure33:Jansenwindingstairssamplingmethod......................................................................71Figure34:Exampleselectionofanadequateproposaldistribution(WORKINPROGRES:IncreaseFontSize)........................................................................................................................73Figure35:Proposedapproachtotransformtheproposaldistribution(U[0,1])intothetargetdistribution(Beta(0.5,0.5))adjuststheproposalsamplessuchthattheweightproposaldistribution(L2Oweighted)matchesthetargetdistribution......................................................74Figure36:Totalfuelburnusingthedecomposition-baseduncertaintyanalysismethodontheBoeing737-800............................................................................................................................75

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ListofTablesTable1:CustomTASOptoutputfile(e.g.,*.dat)requiredforTASOpt-AEDTmodulesintegration.......................................................................................................................................................18Table2:Enginemetaltemperaturedistribution..........................................................................20Table3:Filmcoolingeffectiveness...............................................................................................21Table4:Filmcoolingeffectiveness...............................................................................................21Table5:Compressorpolytrophicefficiencydistribution.............................................................22Table6:Turbinepolytrophicefficiencydistribution....................................................................22Table7:Turbineentrytotaltemperaturedistribution.................................................................22Table8:Overallpressureratiodistribution..................................................................................23Table9:FanPressureratiodistribution.......................................................................................23Table10:Materialstresspropertiesdistribution.........................................................................24Table11:Materialstresspropertiesdistribution.........................................................................24Table12:Materialstresspropertiesdistribution.........................................................................24Table13:Aircraftoperationaldistribution...................................................................................25Table14:AircraftOperationalDistribution..................................................................................25Table15:AEDTSQLFLEETdatabaseentriesfortemporaryTASOptaircraft...............................28Table16:UQstudyAEDTflighttrajectories.................................................................................29Table17:(DataNotFinal)TotalfuelburncomparisonbetweenTASOptandAEDToverthreeflightscenariosandfiveflightsegments......................................................................................59Table18:TASOptandAEDTcomparison;totalfuelburnandrelativepercentuncertainty........59Table19:The17importantinterfacevariablesselectedfromtheO(100)variables...................72

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NomenclatureAbbreviations

AEDT Aviation&EnvironmentalDesignToolASIF AEDTStandardInputFileB738 Boeing737-8000AircraftConfigurationBADA BaseofAircraftDataCAS CalibratedAirspeedCAEP CommitteeforEnvironmentalProtectionCR CruiseD8 DoubleBubbleAircraftConfigurationDE DescentGHG GreenhouseGasGSA GlobalSensitivityAnalysisIC InitialClimbICAO InternationalCivilAviationOrganizationISA InternationalStandardAtmosphereMCS MonteCarloSimulationMSI MainSensitivityIndexMSL MeanSeaLevelMTOW MaximumTakeoffWeightMLW MaximumLandingWeightLD LandingTAS TrueAirspeedTASOpt TransportAircraftSystemOPTimizationTO TakeoffTOW TakeoffWeightTSFC ThrustSpecificFuelConsumptionTSI TotalSensitivityIndexUQ UncertaintyQuantificationX_Y UnitConversionfromXtoY

Notations𝐶! CoefficientofDrag [-]𝐶! Initial-climbcalibratedairspeedcoefficient [-]𝐶! CoefficientofLift [-]

𝐶!,!"# MaximumCoefficientofLift [-]𝐵! Takeoffground-rollcoefficient [-]𝐷! LandingSpeedcoefficient [-]

𝜀!"#,!" LowPressureCompressorPolytrophicEfficiency [-]𝜀!"#,!! HighPressureCompressorPolytrophicEfficiency [-]𝜀!"#,!" LowPressureTurbinePolytrophicEfficiency [-]

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𝜀!"#,!! HighPressureTurbinePolytrophicEfficiency [-]𝐸!"# AirfoilCapModulusofElasticity 𝐸!"#$" AirfoilStrutModulusofElasticity 𝐹𝑃𝑅 FanPressureRatio [-]ℎ Altitude [ft]𝑀 MachNumber 𝑚 FuelFlow [kg/sec]𝑛!"# NumberofEnginesSupplyingThrust 𝑂𝑃𝑅 OperatingPressureRatio [-]𝑃! PressureatMSL [Pa]𝑃 PressureatEngineInlet [Pa]

𝜎!"#$ AircraftSkinYieldStress [MPa]𝜎!"#$ BendYieldStress [MPa]𝜎!"# AirfoilCapYieldStress [MPa]𝜏!"# WebShearYieldStress [MPa]𝜎!"#$" AirfoilStrutYieldStress [MPa]𝑅 Range [nmi]

𝜌!"#$ AircraftSkinYieldStress [MPa]𝜌!"#$ BendYieldStress [MPa]𝜌!"# AirfoilCapYieldStress [MPa]𝜌!"# YieldStress [MPa]𝜌!"#$" AirfoilStrutYieldStress [MPa]𝑆𝑡! StantonNumber [-]𝑇! TemperatureatAirportAltitude [K]𝑇 TemperatureatEngineInlet [K]

𝑇!"#$% AllowableMetalTemperature [K]𝑇!,!" TakeoffTemperatureatEngineInletandAirportAltitude [K]𝑇𝑇!,!" TurbineInlet(Stage4)GasTemperatureatTakeoff [K]𝑇𝑇!,!" TurbineInlet(Stage4)GasTemperatureatCruise [K]Δ𝑇 TemperaturedeviationfromISAatAirportAltitude [K]V AircraftVelocity [knts]𝜆 TemperatureVariationwithAltitude=-0.0065 [K/m]𝜃! Filmcoolingeffectiveness [-]

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Section1

Introduction

As part of the tool development effort the Federal Aviation Administration (FAA) Office ofEnvironment and Energy (AEE) is conducting research to evaluate howuncertainties in inputparameters and assumptions affect the outputs of the analytical tools that comprise theaviation environmental tool suite. As part of this work, AEE is interested in performing asystem-level uncertainty quantification (UQ) analysis. This system-level assessment willquantifyhowuncertaintiesinaircrafttechnologiesanddesignoperationparameterspropagateonto aircraft performance uncertainties and finally uncertainty in total fuel burn and overallpolicyoutcomes.Thefollowingsectionwilloutlinethemotivationandobjectivesoftheworkaswell as describe the standard system-level Monte Carlo simulation (MCS) and thedecomposition-basedUQmethodologies.

MotivationTheaviationsectorisbelievedtobeoneofthefastestgrowinganthropogenicGHGemissions.In2005,aircraftemissionsincreased45%from1992andaccountedforapproximately2.5%ofanthropogenic CO2 emissions and 3.5% of historical manmade radiative forcing (Lee, et al.,2009). Left unconstrained, aircraft emissions could quadruple by 2050 (2010a, 2010). As ameasure to manage the climate impact of aviation, the Committee for EnvironmentalProtection (CAEP) under the International Civil Aviation Organization (ICAO), adopted anaspirational2%annualefficiency improvementgoal foraviation through2050 (2010b,2010).To reduce its CO2 emissions, aviation is pursuing significant enhancements to aviationtechnology, sustainable fuels with low CO2 emissions, and efficient operational procedures(Rutherford&Mazyar,2009).

Tomeetthesedemandingrequirements,CAEPassembledapanelofindependentexpertswithvaryingbackgroundstoestablishlong-termtechnologygoalsforaviationfuelburn(Cumpsty,etal., 2010). Their study investigated future aviation technology scenarios, which representedvaryingregulatorypressuretoreducefuelburn.Thefutureaircrafttechnologyscenarioswerethenappliedinanalysistoolsas“technologypackages”toassessthetechnologyimprovementon aircraft fuel burn. Due to resource limitations the independent experts were unable toaddressthefollowingissues:

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� The impact of uncertainties in aviation technology development on fuel burnperformanceandimplicationsonpolicyassessment.

� The lack in modeling of integration interdependencies between technologies whichcouldnotbehandledbyconceptual-leveltools.

Inthisreport,wewilladdressthesechallengesalongwiththefollowing:

� The impact of uncertainties in aircraft technology and design operations onpredictabilityoffuelburnperformanceandimplicationsonpolicyassessment.

Thesetasksareaccomplishedbyperformingasystem-leveluncertaintyquantificationusingaconceptual-levelaircraftdesigntoolandanaviationenvironmentaldesigntool.Thisreportwillassist in understanding how the uncertainties in aircraft technologies and design operationsintegrate into the uncertainty in the aircraft fuel burn performance while considering theimpactsofaircraftconfigurationsandaviationtechnologicaldevelopments.

MethodologyTheobjectiveofthiseffortistoperformasystem-leveluncertaintyquantification(UQ)analysison a toolset consisting of the Transport Aircraft System OPTimization (TASOpt) (Drela,SimultaneousOptimizationof theAirframe,Powerplant,andOperationofTransportAircraft.,2010) and the Aviation Environment Design Tool (AEDT) Version 2a (Roof, et al., 2007) asdepictedinFigure1usingthestandardsystem-levelMCSUQandnoveldecomposition-basedUQapproaches.

Figure1:System-levelUQofthetoolsetconsistsofquantifyinghowuncertaintyinaircrafttechnologyanddesignoperationsimpactstheuncertaintyintheoutputsofinterest(e.g.,fuelburn).

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TheintentoftheUQanalysis istocharacterizethesystemoutputsof interest(e.g., fuelburnand emissions) distributions due to uncertainties in system inputs (e.g., aircraft technologiesanddesignoperationparameters)aswellasidentifywhichinputshavethegreatestimpactonthe outputs of interest, while accounting for aviation technology development and aircraftconfiguration.Theresultsof thisanalysiscouldbeused, forexample, toassistmanufacturersand designers by prioritizing their research efforts in reducing uncertainty in specific aircrafttechnologies or design mission parameter. Our analysis will investigate three aircraftconfigurations:theBoeing737-800andtheMITDoubleBubble(D8)designwithstandardandadvancedtechnologies(Drela,DevelopmentoftheD8TransportConfiguration,2010).Further,theUQanalysisisperformedusingthenewdecomposition-basedapproachdevelopedatMIT(Amaral,Allaire,&Willcox,2012)andthestandardall-at-onceMCSUQapproach.Thespecificresearchtasksarelistedbelow:

1. Definetheaircraftconfigurations:Boeing737-800,D8(Standard),andD8(Advance).2. Characterizeaircrafttechnologyanddesignoperationuncertaintydistributionsusing

historicaltrendsandengineeringjudgment.3. DevelopamappingfromTASOptaircraftperformancetoAEDTaircraftmetrics.4. Performthesystem-levelMCSuncertaintyquantificationanalysis.5. Performthedecomposition-baseduncertaintyquantificationanalysis.

Theresultswillcharacterizetheoutputsofinterestdistributionandidentifythemostsignificantsources of uncertainty across different aircraft configurations and technologies. Further, theresultswillcomparethestandardsystem-levelMCSUQapproachandthedecomposition-basedUQapproach.

System-LevelUncertaintyQuantificationThe system-level MCS UQ approach is a standard approach to quantifying uncertainty insystems.TheapproachrequiresintegratingallthecomponentsunderoneframeworkasshowninFigure1,fromwhichuncertaintyandsensitivityanalysismaybecomputed.

UncertaintyAnalysisTheobjectiveofuncertaintyanalysisistoanswerthequestion,“Howdouncertaintiesinmodelfactors propagate to uncertainties in model outputs?”. Uncertainties in model outputs arecharacterizedbystatisticsofinterestsuchasmodeloutputmean,variance,andtheprobabilityof an event occurring. These quantitative representations of uncertainty in model outputsprovide a means of comparing various policy scenarios and quantitatively evaluating theperformanceofthemodelrelativetofidelityrequirements.Uncertaintyanalysiscanbecarried

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outwithseveraldifferentmethods,suchasmean-valuemethods,analyticreliabilitymethods,stochastic expansion methods (e.g., polynomial chaos expansion), and sampling-basedtechniques such as Monte Carlo simulation. The approach we selected for this work is thesampling-basedMonteCarlosimulationtechniqueasshowninFigure2.

𝒙! = 𝑥!!, 𝑥!!,… , 𝑥!! 𝒙! = 𝑥!!, 𝑥!!,… , 𝑥!!

⋮𝒙! = 𝑥!! , 𝑥!! ,… , 𝑥!!

𝒚! = 𝑦!!,𝑦!!,… ,𝑦!! 𝒚! = 𝑦!!,𝑦!!,… ,𝑦!!

⋮𝒚! = 𝑦!! ,𝑦!! ,… ,𝑦!!

Figure2:System-leveluncertaintyanalysisusingthesampling-basedtechnique(e.g.,MCS)

TheTASOpt-AEDT systemmapsa k-dimensional input vector𝒙 (e.g.,𝒙 = {EngineEfficiencies,CruiseAltitude,…})intoad-dimensionaloutputvector𝒚(e.g.,𝒚={FuelBurn,CO2,…}).Letthesequence 𝒙!,𝒙!,… ,𝒙! beanindependentidenticallydistributedsetofrealizationsfromtheinputdistributionwhere𝒙! representsthe𝑖!!realization.Anexpectationof𝒚evaluatedusing𝑁realizationsisdefinedas,

𝝁 =1𝑁 𝒚! .

!

!!!

Eq.1

By the strong lawof largenumbers,𝝁weakly converges to𝔼𝒚 𝒚 as𝑁 → ∞. By theCentral

LimitTheorem,theconvergencerateof𝝁totheexpectedvalueof𝔼𝒚 𝒚 isgivenby𝑂 1/ N .VarianceandotherquantitiesofinterestcansimilarlybeestimatedusingMCS.

SamplingMethodsThereareseveralapproachestodrawrealizationsoftherandomvector𝒙.Themostcommonapproaches are pseudo-random sampling and quasi-random sampling. Pseudo-randomsamplingusesacomputer’spseudo-randomnumbergeneratortodrawrealizationasshownonthe left of Figure 3. Quasi-random sampling selects samples deterministically using a low-discrepancysequence,whichattemptstodrawrealizationsfromaspaceuniformlyasshownontherightofFigure3.Fortheuncertaintyanalysis,quasi-randomsamplingwasselectedsinceitsconvergencerateis𝑂 log N !/N ,where𝑘 isthenumberof inputdimensions(Niederreiter,1992).

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Figure3:Uniformsampling(Left:Pseudo-Random)(Right:Quasi-Random)

GlobalSensitivityAnalysisThe second component of uncertainty quantification is global sensitivity analysis (GSA). ThemotivationforGSAistoprioritizeresearchandtosimplifythemodel(AndreaSaltelli,2008).

� Prioritizeresearch:Whichfactorsaremostdeservingoffurtheranalysis?

� Modelsimplification:Cansomefactorsofthemodelbefixed?

TheGSAmethodselectedforouranalysisisavariancebasedmethod.Variancebasedmethodsdecomposetheoutputvariance intocontributions from individualmodelparametersandtheinteractionsbetweenparametersasshowninFigure4. Variancebasedmethodscalculateanaveragedglobalcontributiontooutputvariancefromeachfactor,whichincludesallinteractioneffectsamongthedifferent factors.That is, it includesanyeffectsthatoccurbytwoormorefactors directly affecting each other. For this assessment, the Sobol’ method, discussed inAppendix A, is used to compute the expected global contribution represented as the totalsensitivity index (TSI).TheTSIquantifies the impactan inputand thedistributionassignedtothat input have on the variance of a specific output. TSI is defined as the output variancecausedbyagiven factorand its interactions,dividedby thetotaloutputvariance.Therefore,thelargerafactor’sTSI,thelargerimpactithasonthevarianceoftheoutput.Mainsensitivityindices (MSI) quantify the impact the input without interaction effects and the distributionassignedtothat inputhaveonthevarianceofaspecificoutput.Therefore,MSI isalwayslessthanorequaltoTSIandbothvaluesarelessthanorequaltoone.

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Figure4:Globalsensitivityanalysisvariancedecomposition(Allaire,2009)

Theoutcomeofaglobalsensitivityanalysisistoidentifyandrankthefactors’influenceontheoutputvariance.Thisinformationallowstheusertoprioritizetheirfutureresearcheffortsandperform factor fixing. Understanding which inputs have the largest influence on the outputvariance would guide future research efforts in reducing the input variance through stricteranalysisor improvedunderstanding.Factorfixingallowstheusertoreducethecomplexityofthemodelinputsbyidentifyingthosefactorsthatoncefixedhavenegligibleimpactonoutputvarianceandcanthereforebetreatedasdeterministic.

Decomposition-BasedUncertaintyQuantificationIn some scenarios it may be challenging to conduct UQ of systems comprising multiplecomponents. In such cases, the models may be developed by different groups and run ondifferentcomputationalplatforms.Inaddition,themodelsmaynotbeseamlesslyintegratedinan automated fashion. Existing UQ methods typically involve coupling the models andperforming a system-level MCS uncertainty and sensitivity analysis. This approach, whileadequate in some situations, emphasizes joiningmultiplemodels under one group,which isundesirableandeveninfeasibleinmanycases.Inthisworkweproposetodevelopadifferentapproach for systemUQ that involves decomposition of theUQ task, performingUQon therespective models individually, and reassembling model-level information to quantifyuncertainty at the system level. Our approach enables a new view to system UQ, throughdecomposition of the system-level UQ into a set of manageable model-level UQ analysesfollowedbysynthesizingtheinformationatthesystemlevelinaprovablyconvergentmanner.

UncertaintyAnalysisIn the case of uncertainty analysis, the decomposition-based approach is composed to twomain procedures: (1) Local uncertainty analysis: perform a local Monte Carlo uncertaintyanalysis on each discipline over their respective proposal input distributions; and (2) Global

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compatibility satisfaction: reweight the individual discipline Monte Carlo proposal samplessuchthat thereweightedsamplesapproximatethe target inputdistributions tosatisfyglobalcompatibility constraints. We use the terms proposal distribution to refer to the inputdistributionassumedatthelocallevelforeachdiscipline,andtargetdistributiontorefertotheactual input distributionwhen system compatibility constraints are satisfied (e.g., the targetdistribution might be specified through the output distribution of an upstream discipline).Throughthesetwostepsitispossibletopropagateinputuncertaintiesfromthesysteminputstosystemoutputsofinterestinamannerthatisprovablyconvergent.TheideaoftheapproachisillustratedinFigure5[9].

Figure5:Theproposedmethodofmulticomponentuncertaintyanalysisdecomposestheproblemintomanageable components; similar to decomposition-based approaches used in multidisciplinaryanalysisandoptimization,andsynthesizethesystemuncertaintyanalysiswithoutneedingtoevaluatethesysteminitsentirety.

SensitivityAnalysisThedecomposition-based global sensitivity analysis, illustrated in Figure6, resolves themainsensitivityindicesofthesystembybuildinguponthedecomposition-baseduncertaintyanalysisresults.Futureresearchefforts includeassessing 2ndandhigherordersensitivity indicesbyadecomposition-basedapproach.

Figure6:Illustrationoftheproposedmethodfordecomposition-basedglobalsensitivityanalysis.

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Section2

TASOpt

The TASOpt module is an aircraft performance tool developed by Prof. Mark Drela at MIT.TASOpt allows users to evaluate future aircraft with potentially unconventional airframe,aerodynamic,engine,oroperationparametersusing low-orderphysicalmodels implementingfundamental structural, aerodynamic, and thermodynamic theory. It uses historical basedcorrelationsonlywhennecessary, inparticularonly for someof the secondary structureandaircraft equipment. The TASOpt module takes as input aircraft technology and operationalparametersandcanoptimizeanaircraftoveragivensetofconstraintsorresizeanaircrafttomeetthedesiredmissionrequirements.

SourceCodeModificationsThe TASOptmodule required slightmodifications to the source code in order to integrate itwiththeAEDTmodule.Thesemodificationsarediscussedbelow.

MissionInputsToextracttheAEDTaircraftperformancemetricsfromtheTASOptaircraftperformancemetricsrequiressimulatingaparticularaircraftdesignovermultiplemissionscenarios.Therefore,thesource codes getval.f and getparam.f are modified so that TASOpt may simulate up to 100mission scenarios. The source file getparam.f was modified to include cutback sight angle,cutback climb angle, top descent angle, bottom descent angle, cruise coefficient of lift, andcruiseMachnumberasextramissionparameters.

AirportTemperatureTheAEDTmodulecontainsaircraftperformancecorrelations thatarea functionofchange intemperaturefromISA.Therefore,theTASOptinputfile(e.g.,*.tas)wasmodifiedsuchthatthetemperature at the airport is a change in temperature from ISA instead of an absolutetemperatureattheairport.Forexample,aT!,!" = 0 [𝐾]isequivalenttoISAconditionsattheairportaltitudeandT!,!" = 10 [𝐾] isequivalent to ISAconditionsat theairportaltitudeplus10 [𝐾].

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AtmosphericConditionsThesourcecodeatmos.fwasmodifiedsothattheatmosphericconditionsareequivalenttotheAEDT2aatmosphericconditions(Manual,2012).ThecodewasalsomodifiedtoaccountforachangeintemperaturefromISAconditionsattheairportaltitudeasshown,

𝑇 ℎ =𝑇! − 𝜆 ∙ 3280.84 ∙ ℎ

1.8 + Δ𝑇,

Eq.2

𝑃 ℎ = 𝑃! ∙1− 𝜆 ∙ 3280.84 ∙ ℎ

518.67

!.!"#

∙1

0.0393701 ∙101.325760.0 ∙ 1000.

Eq.3

Thesourcecodeswhichcallatmos.fweremodifiedtotakeinthevariableΔ𝑇.Thesourcecodesmodifiedinclude:fusebl.f,getparm.f,mission.f,output.f,tasopt.f,woper.f,andwsize.f.

CruiseFlightThesourcefilemisson.fwasmodifiedsothatthefirstcruisepointisevaluatedwithrespecttoitscurrentaltitudeandatmosphericconditions.Theatmosphericconditionsatthefirstcruisepointarethenusedtoinitializetheenginevariablesasisdoneforthelastcruisepoint.

InitializeEngineThe source codewoper.f wasmodified so that was engine parameters are initialized to thedesignengineparametersbeforeinitializingtotheknownoperatingconditions.

PerformanceOutputThesourcecodeoutput.fwasmodifiedtoprintoutacustomoutputfilewhichsimplifiedtheTASOptandAEDTintegration.ThisoutputfilecontainsthenecessaryaircraftperformancemetricsandisformattedasshowninTable1.

Table1:CustomTASOptoutputfile(e.g.,*.dat)requiredforTASOpt-AEDTmodulesintegration.

MTOW =185810.8 lb Wempty =93909.8 lb WfuelM =64103.2 lb S =1476.9 ft2 Fmax =127.86 kN Mission Profile 1

R[nmi] h[ft] ⋯ Feng[kN] mdotf[kg/sec] ⋯ MachST 1 0.0 0.0 ⋯ 127.86 2.794 ⋯ 0.000TO 1 0.0 0.0 ⋯ 103.66 2.855 ⋯ 0.258⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮D5 1 3000.0 0.0 ⋯ 6.64 0.238 ⋯ 0.225

Mission Profile 2 R[nmi] h[ft] ⋯ Feng[kN] mdotf[kg/sec] ⋯ MachST 2 0.0 105.0 ⋯ 125.83 2.753 ⋯ 0.000⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮

19

AircraftConfigurationTheaircraftconfigurationsselectedforthisstudyaretheBoeing737-800andMITD8.TheMITD8 is a concept aircraft designed atMIT by Prof.MarkDrela (Drela,Development of theD8TransportConfiguration,2010).TheMITD8aircraftwasdevelopedtooperateintheshort-tomedium range while seating 180 passengers similar to the Boeing 737-800. The aircraftconfigurationsareshownforcomparisoninFigure7.

Figure7:Boeing737-800andMITD8airframeconfigurations[6]

Thisstudyalsoconsiders the impactsofaviation technologyenhancementsusing theMITD8configuration. Future technologyenhancements include improvedaircraftengineefficiencies,aircraft engine materials, and light-weight carbon fiber components. For each aircraftconfiguration,wefirstusetheTASOptmoduletooptimizetheaircraftsovertheirrespectivesetofvariablesforamissionconsistingofa3000[nmi]rangewithapayloadweightof40,500[lb]atISAconditions.Theresultingoptimalaircraftconfigurationthenbecomesthedesignaircraftfromwhich the UQ study is performed. The optimal design aircraft TASOpt input files (e.g.,B737.tas)aregiveninAppendixB.TheseTASOptinputfilesrepresenttheoptimalconfigurationandcontainplaceholdersfortheuncertainparameters.Givenrealizationsfromtheuncertainparameterdistributions,theTASOptinputfileispopulated;afterwardsTASOptsizestheaircraftbeginningfromtheoptimaluncertainconfigurationtomeetthedesiredmissionscenarios.

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TASOptInputParametersThissectionwilldescribethe27uncertainparameters includingtheirrespectivedistributions.ThesectionwillalsopresentthemissionparametersweeprequiredtoextracttheAEDTaircraftperformancemetricsfromtheTASOptaircraftperformancemetrics.

UncertaintyDistributionsThe following uncertain distributions are the 27 uncertain parameters selected for the UQstudy.ArealizationfromthesedistributionspopulatesthefirstmissionwhichTASOptusestoappropriately size the aircraft. This random aircraft is then flown over multiple missions toextractthedesiredinformationrequiredbyAEDT.

EngineMetalTemperature(𝑻𝒎𝒆𝒕𝒂𝒍)The engine metal temperature determines the temperature the engine blade material canwithstandonaverage.Forexample,ahighmetaltemperatureenginerequireslesscoolantthena low metal temperature engine and therefore is more efficient. Figure 8 illustrates thetemperaturecapacityofmaterialscommonlyusedinaircraftengines(Kyprianidis,2011).Whilethe standard technology aircraft metal temperatures are reasonable, the D8 advancedtechnologywouldrequireasignificant improvement intechnologytoobtaina1500[K]metaltemperature.Theuncertaintyinenginemetaltemperaturecapacityrepresentsouruncertaintyinmaterialpropertiesandmeasurements.

Table2:Enginemetaltemperaturedistribution

Name Units Distribution Boeing737-800 StandardD8 AdvancedD8𝑇!"#$% [K] U[-50,50] 1222 1200 1500

Figure8:Historicaltrendsforenginemetaltemperaturecapacity(Kyprianidis,2011)

21

FilmEffectiveness(𝜽𝒇)Thefilmeffectivenessisdefinedasfollows,

𝜃! =𝑇! − 𝑇!"#𝑇! − 𝑇!"

,

Eq.4

where𝜃!isthefilmeffectiveness,𝑇!isthehotgasfluidtemperature,𝑇!"isthecoolgasfluidtemperatureexiting the filmhole,and𝑇!"# is thehypotheticaladiabaticwall temperature. If𝜃! = 1, the cooling fluid covers the blade and if 𝜃! = 0, the cooling flow is absent. Theuncertaintyinfilmeffectivenessrepresentsouruncertaintyinmanufacturingcoolingholesandthesupplyanddumppressures.

Table3:Filmcoolingeffectiveness

Name Units Distribution Boeing737-800 PresentD8 FutureD8𝜃! [-] U[-0.005,0.005] 0.32 0.30 0.4

StantonNumber(𝑺𝒕𝒄)TheStantonnumberisdefinedasfollows,

𝜂 =𝑇!" − 𝑇!"𝑇! − 𝑇!"

= 1− 𝑒𝑥𝑝 −𝐴!"𝐴!

𝑆𝑡! ≅ 0.7,

Eq.5

where𝜂isthecoolingefficiency,𝑆𝑡! istheStantonnumber, 𝑇! isthemetaltemperature,𝑇!" isthecoolgasfluidtemperatureenteringthefilmhole,𝐴! isthecoolingflowarea,and𝐴!"isthecooling hole heat transfer area. A low Stanton number indicates a better film coolingtechnologywhichdrawsmorecoolair tothehotsurface.Theuncertainty inStantonnumberrepresents our uncertainties in manufacturing film cooling holes and the supply and dumppressures.

Table4:Filmcoolingeffectiveness

Name Units Distribution Boeing737-800 PresentD8 FutureD8𝑆𝑡! [-] U[-0.001,0.001] 0.095 0.09 0.065

CompressorPolytrophicEfficiency(𝜺𝒑𝒐𝒍,𝒍𝒄/𝜺𝒑𝒐𝒍,𝒉𝒄)Thecompressorpolytrophicefficiencyaccountsforthenon-isentropiccompressionprocess.Ahigh compressor polytrophic efficiency results in amore efficient engine. The uncertainty incompressor polytrophic efficiencies represents our uncertainty attributed to measuringcompressorefficiencywhileinoperationandcomponentmanufacturing.

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Table5:Compressorpolytrophicefficiencydistribution

Name Units Distribution Boeing737-800 PresentD8 FutureD8𝜀!"#,!" [-] U[-0.001,0.001] 0.937 0.92 0.93𝜀!"#,!! [-] U[-0.001,0.001] 0.904 0.89 0.9

TurbinePolytrophicEfficiency(𝜺𝒑𝒐𝒍,𝒍𝒕/𝜺𝒑𝒐𝒍,𝒉𝒕)Theturbinepolytrophicefficiencysimilartothecompressorpolytrophicefficiencyaccountsforthenon-isentropicprocessbutfortheturbinesectionoftheengine.

Table6:Turbinepolytrophicefficiencydistribution

Name Units Distribution Boeing737-800 PresentD8 FutureD8𝜀!"#,!" [-] U[-0.001,0.001] 0.871 0.91 0.925𝜀!"#,!! [-] U[-0.001,0.001] 0.876 0.92 0.93

TurbineEntryTemperature(𝑻𝑻𝟒,𝑻𝑶/𝑻𝑻𝟒,𝑪𝑹)Theturbineentrytemperaturedefinesthegastemperatureenteringtheturbinecomponentofthe aircraft engine. Figure 9 shows the historical and the extrapolated turbine inlet gastemperatures. The uncertainty associated to turbine entry temperatures are measurementuncertaintiesandvariabilityinupstreamcomponents.

Table7:Turbineentrytotaltemperaturedistribution

Name Units Distribution Boeing737-800 PresentD8 FutureD8𝑇𝑇!,!" [K] U[-50,50] 1833 1576 1709𝑇𝑇!,!" [K] U[-50,50] 1591.5 1335 1506

Figure9:Historicaltrendsforturbineentrytotaltemperature(Kyprianidis,2011)

23

OverallPressureRatio(𝑶𝑷𝑹)The overall pressure ratio corresponds to the pressure ratio between the exit of the highpressure compressor and the atmospheric pressure. Figure 10 shows the historical overallpressureratioinrelationtoentryofservice.Theuncertaintyassociatedtotheoverallpressureratiorepresentsouruncertaintyinmeasurementandvariabilityinmanufacturingcomponents.

Table8:Overallpressureratiodistribution

Name Units Distribution Boeing737-800 PresentD8 FutureD8𝑂𝑃𝑅 [-] U[-2.0,2.0] 26.2 35 50

Figure10:Historicaltrendsforengineoverallpressureratio(Gunston,1998)

FanPressureRatio(𝑭𝑷𝑹)The fan pressure ratio is equal to the pressure ratio between the outlet of the fan and theatmospheric pressure. The standard technology configurations use conventional direct driveturbofanwhereastheadvancedtechnologyconfigurationwoulduseagearedturbofanwhichallows for a lower fan pressure ratio and higher propulsive efficiency. The uncertaintyassociated to the fan pressure ratio is our uncertainty in measurement and variability inmanufacturingcomponents.

Table9:FanPressureratiodistribution

Name Units Distribution Boeing737-800 PresentD8 FutureD8𝐹𝑃𝑅 [-] U[-0.001,0.001] 1.61 1.6108 1.39262

24

MaterialStressProperties(𝝈𝒔𝒌𝒊𝒏,𝝈𝒃𝒆𝒏𝒅,𝝈𝒄𝒂𝒑, 𝝉𝒘𝒆𝒃,𝝈𝒔𝒕𝒓𝒖𝒕)The material stress properties are the fuselage pressurization skin stress 𝜎!"#$ , fuselagebending skinandstringer stress 𝜎!"#$ ,wing/tailbendingcaps 𝜎!"# ,wing/tailwebs shearstress 𝜏!"# , and strut stress 𝜎!"#$" . These uncertainties are associated to measurementaccuracy.

Table10:Materialstresspropertiesdistribution

Name Units Distribution Boeing737-800 PresentD8 FutureD8𝜎!"#$ [psi] U[-5%,5%] 15000 15000 29800𝜎!"#$ [psi] U[-5%,5%] 30000 30000 49500𝜎!"# [psi] U[-5%,5%] 30000 30000 39700𝜏!"# [psi] U[-5%,5%] 20000 20000 21300𝜎!"#$" [psi] U[-5%,5%] 30000 30000 66000

MaterialModulusofElasticityProperties(𝑬𝒄𝒂𝒑,𝑬𝒔𝒕𝒓𝒖𝒕)Thematerialmodulusofelasticitypropertiesarethewingsparcapmodulusofelasticity 𝐸!"# and strutmodulus of elasticity 𝐸!"#$" . These uncertainties are associated tomeasurementaccuracy.

Table11:Materialstresspropertiesdistribution

Name Units Distribution Boeing737-800 PresentD8 FutureD8𝐸!"# [psi] U[-5%,5%] 10e6 10e6 18.2e6𝐸!"#$" [psi] U[-5%,5%] 10e6 10e6 7.5e6

MaterialDensityProperties(𝝆𝒔𝒌𝒊𝒏,𝝆𝒃𝒆𝒏𝒅,𝝆𝒄𝒂𝒑,𝝆𝒘𝒆𝒃,𝝆𝒔𝒕𝒓𝒖𝒕)The material density properties are the fuselage skin density ρ!"#$ , fuselage bendingskin+stringer density ρ!"#$ , wing/tail bending cap density ρ!"# , wing/tail web densityρ!"# , and strut density ρ!"#$" . These uncertainties are associated to measurementaccuracy.

Table12:Materialstresspropertiesdistribution

Name Units Distribution Boeing737-800 PresentD8 FutureD8𝜌!"#$ [psi] U[-1%,1%] 2698.8 2698.8 1550.1𝜌!"#$ [psi] U[-1%,1%] 2698.8 2698.8 1550.1𝜌!"# [psi] U[-1%,1%] 2698.8 2698.8 1550.1𝜌!"# [psi] U[-1%,1%] 2698.8 2698.8 1550.1𝜌!"#$" [psi] U[-1%,1%] 2698.8 2698.8 1550.1

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OperationalUncertainties(𝒉𝑪𝑹,𝑪𝑳,𝒎𝒂𝒙,𝑪𝑳,𝑴)Theoperationalparametersincludethecruisealtitude,maximumcoefficientoflift,coefficientof lift at cruise, and cruise Mach number. These uncertainties represent the uncertainty adesignerwouldhaveinthedesignofanaircraftforatypicalflightoperationscenario.

Table13:Aircraftoperationaldistribution

Name Units Distribution Boeing737-800 PresentD8 FutureD8ℎ!" [ft] U[-1000,1000] 35000 39911 42838𝐶!,!"# [-] U[-0.05,0.05] 2.25 2.15 2.5𝐶! [-] U[-0.01,0.01] 0.57714 0.6945 0.70476𝑀 [-] U[-0.01,0.01] 0.78 0.72 0.74

MissionParametersAfter obtaining a single realization vector from the 27 input distributions, the remaining 99missions are generated using a design of experiments. A Latin hypercube sampling schemeprovides the remaining 99 missions in order to quantify the aircraft performance undermultiple mission scenarios. The mission parameters selected along with their respectiveparametersweepsaregiveninTable14.Foraparticularvariable(e.g.,𝑅),Eq.6describeshowthe variable varies given the center, span, and Latin hypercube value for the variable, Χ! ∈0,1 .Forexample,therangevariableisexpectedtosweepfrom750[nmi]to3250[nmi].

𝑉𝑎𝑙𝑢𝑒 = 𝐶𝑒𝑛𝑡𝑒𝑟 + (Χ− 0.5) ∙ 𝑆𝑝𝑎𝑛. Eq.6

Table14:AircraftOperationalDistribution

Name Units Center[Boeing737-800/D8] Span𝑅 [nmi] 2000 2500

𝑊!"# [lb] 215 100ℎ!" [ft] 0.0 8000Δ𝑇 [K] 0.0 25ℎ!" [ft] RandomVariable 8000𝐶!,!"# [-] RandomVariable 0.1Θ!" [deg] 40.0 2.0Θ!" [deg] 3.0 0.4Θ!",! [deg] [-3.0/-2.0] 0.4Θ!",! [deg] [-3.0/-2.5] 0.4C! [-] RandomVariable 0.05𝑀 [-] RandomVariable 0.04

26

The TASOpt module steps are shown in Figure 11. Starting from the optimal aircraftconfiguration (e.g., blue aircraft), 27 temporary place holders located in the 1st mission arereplacedby27realizationseachdrawnfromtheirrespectiveuncertaindistributions.These27randomvariablesdescribeanewaircraftconfigurationwhich issimilartotheoptimalaircraftconfigurationbutcharacterizesourlackofknowledgeregardingthe27inputvariables.TASOptthenresizesthenewaircraftconfigurationtomeetthefirstmissionwhichiscommonamongallaircraft configurations (e.g., red aircraft). The remaining 99missions, described by the LatinHypercube,usetheresizedaircraftfromthefirstmission.TheresultsproducedbyTASOptoverthese100missionsaretransformedintoAEDTperformancecoefficientsinordertogenerateasimilaraircraftinAEDT.

Figure11:Startingfromtheoptimalaircraftconfiguration(blueaircraft)weincorporateuncertaintiesto characterize the lack of knowledge in aircraft technology and design operations. The new(uncertain realization) aircraft is resized to meet the desired first mission flight specification (redaircraft). The (red) aircraft is then flownovermultiplemission scenarios to extra the aircraft flightperformance.ThisinturnisthenimportedintotheAEDTSQLFLEETDatabasetocreateanequivalentaircraftinAEDT.

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Section3

AEDT

TheAviationEnvironmentalDesignTool(AEDT)modelsaircraftperformanceinspaceandtimetoestimatefuelconsumption,emissions,andnoise.AEDTalsoprovidesuserswiththeabilitytoassess the interdependencies among aviation-produced fuel consumption, emissions, andnoise. HereweusetheAEDTVersion2a.Thisstudywillfocusonfuelconsumptionwhichforcruise conditions relies on the EUROCONTROL’s Base of Aircraft Data (BADA) version 3.10(BADA, 2012). The BADA fuel consumptionmodel uses an energy-balance thrustmodel andThrust Specific Fuel Consumption (TSFC) modeled as a function of airspeed. The BADA fuelconsumption model has been shown to work well in cruise, with differences from airplanereportedfuelconsumptionofabout5%.Forterminalconditions(e.g.,departure/arrivalflightsuntil10,000[ft]abovegroundlevel),AEDT2aderivedanewsetofenergy-balanceequationstosupportahigherleveloffidelityinfuelconsumptionmodeling.

AEDTFleetDatabaseToimprovethecomputationalruntimeoftheAEDTmoduleitisnecessarytoevaluatemultipleaircraft realizations at a given time. To do this will recommend creating 1000 temporaryaircraftsintheAEDTSQLFleetdatabase.ThisstepinvolvesidentifyingthefleetdatabasetablesusedbyAEDTtorepresentauniqueaircraft.TheSQLFLEETdatabasetables includinguniqueidentifiersrequiredtocreateuniqueaircraftarelistedinTable15.

To populate 1000 temporary aircraft the recommended approach is to extract from the SQLFLEET database the tables listed in Table 15 belonging to an aircraft which is similar to thedesiredtemporaryaircraft(e.g.,Boeing737-800).UsingasoftwarepackagesimilartoMicrosoftExcel,eachtableisduplicated1000timesandmodifiedtohaveuniqueidentifierssothattheaircraft does not duplicate an existing aircraft identifier while being sure that the aircraft’sinterconnecting identifiersareconsistent.Withthetablesproperlypopulated,each individualtable,whichnowincludes1000aircraft,aresavedasacommaseparatedvaluesfileandnamedaccording to their respective SQL FLEET database table (e.g., FLT_ACTYPES.csv). Appendix Cprovides thescriptsnecessary to import thecommaseparatedvalue files into theSQLFLEETdatabases.Withtheaircraftproperlypopulated intheSQLFLEETdatabase, theusermayuseanyofthetemporaryaircraftintheirAEDTsimulations.

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Table15:AEDTSQLFLEETdatabaseentriesfortemporaryTASOptaircraft.

FLEETDatabaseTableName Identifier Type[dbo].[FLT_REF_ICAO_ACTYPES] ZZ000–ZZ999 ACTYPE[dbo].[FLT_ACTYPES] ZZ000–ZZ999 ACTYPE[dbo].[FLT_AIRFRAMES] 1000-1999 AIRFRAME_ID[dbo].[FLT_REF_ACCODES] ZZ000-1–ZZ999-1 ACCODE[dbo].[FLT_AIRFRAME_ACTYPE_MAP] ZZ000–ZZ999 ACTYPE[dbo].[FLT_BADA_ACFT] ZZ000–ZZ999 BADA_ID[dbo].[FLT_ANP_AIRPLANES] MIT0–MIT999 ACFT_ID[dbo].[FLT_EQUIPMENT] 5000–5999 EQUIP_ID[dbo].[FLT_DEFAULT_ENGINES] 10000–10999 DEF_ENG_ID[dbo].[FLT_FLEET] 60000–60999 FLEET_ID[dbo].[FLT_DISPERSION] 5000–5999 DISPERSION_ID[dbo].[FLT_BADA_CONFIG] ZZ000–ZZ999 BADA_ID[dbo].[FLT_BADA_FUEL] ZZ000–ZZ999 BADA_ID[dbo].[FLT_BADA_APF] ZZ000–ZZ999 BADA_ID[dbo].[FLT_BADA_ALTITUDE_DISTRIBUTION] ZZ000–ZZ999 BADA_ID[dbo].[FLT_BADA_THRUST] ZZ000–ZZ999 BADA_ID[dbo].[FLT_ANP_AIRPLANE_FLAPS] MIT0–MIT999 ACFT_ID[dbo].[FLT_ANP_AIRPLANE_PROFILES] MIT0–MIT999 ACFT_ID[dbo].[FLT_ANP_AIRPLANE_PROCEDURES] MIT0–MIT999 ACFT_ID[dbo].[FLT_ANP_AIRPLANE_PROCEDURES_EXT] MIT0–MIT999 ACFT_ID[dbo].[FLT_ANP_AIRPLANE_THRUST_JET] MIT0–MIT999 ACFT_ID[dbo].[FLT_ANP_AIRPLANE_TSFC_COEFFICIENTS] MIT0–MIT999 ACFT_ID[dbo].[FLT_ACTYPE_CARRIER] ZZ000–ZZ999 ACTYPE[dbo].[FLT_REF_ANP_EQUIPMENT_DEFAULT] MIT0–MIT999 ANP_AIRPLANE_ID[dbo].[FLT_ANP_BADA_ENERGYSHARE] MIT0–MIT999 ANP_AIRPLANE_ID

FlightTrajectoryTocomparetheuncertaintyquantificationresultswithoneanother,deterministicAEDTflighttrajectorieswereselectedandusedforallthescenariosflownintheAEDTmodule.Theflighttrajectories were selected from a 2006 representative day flight scenario database(Administration, 2013). Using the representative day, the flights associated with the Boeing737-700aircraftwereextractedaspossibleflighttrajectoriessincetheBoeing737-800wasnotcomprehensively represented in the 2006 day flight scenario database. Of the 900 possibleflight trajectories (e.g., departure – arrival airport combinations), for computational resourcepurposes,only20flighttrajectorieswereselected.The20flighttrajectoriesaregiveninTable16 and shown in Figure 12. For simplification purposes, these flight trajectories areapproximatedusingagreatcirclepathfromthedepartureairporttothearrivalairport.

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Table16:UQstudyAEDTflighttrajectories

Flight DepartAirport DepartRunway ArrivalAirport ArrivalRunway Range[nmi]1 KDTW 04L KPVD 23 5352 KIAH 26L KLAX 24L 11973 KLGA 22 KMEM 27 8354 KDTW 04L KSFO 28R 18015 KPDX 28R KLAX 24L 7256 KMIA 08L KDEN 35R 14827 KPDX 28L KABQ 08 9648 KJFK 31R KLGB 16L 21389 KIAD 01R KORD 28 51110 KPHX 26 KMSP 35 110611 KBWI 28 KFLL 09L 80612 KPHX 26 KFLL 09L 171013 KMCO 35L KDCA 01 66214 KIAH 26L KBOS 27 138715 KMCO 17R KMKE 07R 92816 KSJC 30R KIAD 19L 208217 KSFO 28L KPHX 25L 56518 KDFW 35L KSFO 28R 127019 KPHL 09R KFLL 09L 86420 KCLE 24L KSFO 28R 1874

The flight procedureused in this studywas theAEDT sensorpath flight procedure.A sensorpath flight procedure requires the aircraft’s latitude, longitude, altitude, and true airspeedalong the flightpath fromdepartureairport toarrival airport.Using theTASOptmoduleandrespectiveoptimalaircraftconfigurations,thesensorpathdatapointsweregeneratedbyflyingeach optimal aircraft in TASOpt over the ranges specified in Table 16. The resulting TASOptoutputwhichincludeddistance,altitude,andtrueairspeedareconvertedtosensorpathdatapointsandformattedintoanAEDTStandardInputFile(ASIF).WiththeASIF,showninAppendixC,anAEDTStudycanbecreatedandinitialized.WhenanAEDTStudyisgeneratedsoaretheSQLdatabasesbelongingtotheAEDTStudy.Therefore,ausermaynowmodifyexistingaircraftin theAEDTStudybymanipulating theSQLdatabases. For computationalpurposes, theASIFshowninAppendixConlyimportsasingleaircraft(e.g.,MIT0).However,thegoalistosimulate1000aircraftsimultaneouslyinAEDT.Therefore,theoperationsbelongingtothesingleaircraft(e.g., MIT0) are duplicated 999 times for the remaining aircraft (e.g., MIT1 – MIT999). ToduplicatetheoperationstwoupdateSQLscriptsarerequired;onescriptupdates[TEST].[dbo].[AIR_OPERATION_AIRCRAFT] and another script updates [TEST].[dbo].[AIR_OPERATION] asdescribedinAppendixD.

30

Figure12:AEDTUQ20greatcircleflighttrajectories

AEDTRunStudyAtthispointintheanalysistheAEDTStudycontains1000uniqueaircraftconfigurationsand20flight trajectorieswhichwill result in20,000 individual flights.With theAEDTstudy loaded inthe SQL database all other operations regarding pre-processing, simulation, and post-processing can be performed without the AEDT graphical user interface. For propose ofdemonstrationwewillassumetheAEDTstudyisnamed“B738”.

Before executing theAEDT study,wewould need tomodify the 1000 aircraft configurationscurrentlyintheAEDTstudyfleetdatabasetorepresent1000aircraftconfigurationrealizationsfrom the UQ results. Modifying these aircraft requires generating the individual AEDTcoefficients which would represent the aircraft, followed by importing the data into theappropriate place holders in the AEDT study FLEET database. To import data into the AEDTStudyFLEETdatabaseinbatchmoderequiresthefollowingcommand,

sqlcmd-E-SB738-iDATA.sql

where“B738”istheSQLdatabaseservername,automaticallynamedaftertheAEDTstudy,and“DATA.sql” is theSQL file informationregarding the1000aircraft realizations.TheprocessofgeneratingtheseAEDTaircraftrealizationsisdiscussedinSection2.

PriortorunningAEDTinbatchmodetheAEDTresults,iftheyexist,needtobedeleted.ThisisdoneusingthefollowingcommandwhileintheAEDTfolder(e.g.,C:/AEDT).

./FAA.AEE.AEDT.RemoveResults.exeNAMEB738ALL

31

ToruntheAEDTstudyinbatchmode,usethefollowingcommandwhileintheAEDT_RunStudyfolder(e.g.,C:/AEDT_RunStudy).

./FAA.AEE.AEDT.RunStudyB738/a=C:/AEDT ToreadtheAEDToutputdataintheAEDTSQLdatabasesrequiresconvertingtheresultsfrombinarytotextusingapost-processingcommandwhileintheAEDTfolder(e.g.,C:/AEDT).

./FAA.AEE.AEDT.DeserializeEmissions.exeB7381 Finally,toextractthetextresultsoutoftheAEDTSQLdatabaserequiresthefollowingSQLscript.

SET NOCOUNT ON; SELECT s.[CASE_ID], e.[mode], e.[FUEL_BURN], e.[CO2], e.[CO], e.[NOX] FROM [B738].[dbo].[RSLT_EMISSIONS] e JOIN [B738].[dbo].[EVENT_RESULTS_SOURCE] s ON e.EVENT_RESULTS_SOURCE_ID = s.EVENT_RESULTS_SOURCE_ID JOIN [B738].[dbo].[AIR_OPERATION] o ON s.AIR_OP_ID = o.AIR_OP_ID JOIN [B738].[dbo].[AIR_OPERATION_AIRCRAFT] a ON o.AIRCRAFT_ID = a.AIRCRAFT_ID JOIN [B738].[dbo].[FLT_EQUIPMENT] f ON a.EQUIPMENT_ID = f.EQUIP_ID WHERE s.JOB_ID = 1 AND e.EMISSIONS_TYPE = 53 AND f.ANP_AIRPLANE_ID = 'MITXXX' Here‘MITXXX’representsanaircraftofinterestselectedoutofthe1000aircraftrealizationssimulatedbyAEDT.AusermayalsoextractthetextresultsfromtheSQLdatabaseinbatchmodeusingasimilarcommandtothatusedforimporting1000aircraftconfigurationsintotheAEDTStudyFLEETdatabase.

32

Section4

TASOpt-AEDTConnection

Thischapterpresents theprocessof transferring theTASOptaircraftperformanceoutputs toAEDTaircraftperformanceinputs.ThefirstsectiondiscussestheformatoftheTASOptoutputandAEDTinput.ThesecondsectionwillderivetherelationshipbetweenTASOptoutputsandAEDTinputs.ThefinalsectionvalidatesthetransformationbycomparingtheresultsobtainedfromTASOptandAEDToversimilarflightpaths.

DataFormatTheTASOptoutputwaspreviouslyshowninTable1.Theoutputfilecontainsthefollowingvectorwhichdefinestheaircraftstructure,

𝚨 =

𝑀𝑇𝑂𝑊 𝑙𝑏𝑊!"#$% 𝑙𝑏𝑊!"#,!"#$ 𝑙𝑏

𝑆 𝑓𝑡!𝐹!"# [𝑘𝑁]

. Eq.7

Theoutputfilealsocontainsamatrixwith1500rows(100missionsby15flightsegments)by12columns. The 15 flight segments consist of 3 takeoff segments, 5 climb segments, 2 cruisesegments,and5descentsegmentsasshowninFigure.

Figure13:TASOptflightsegmentbreakdown.

33

Foragivenmission𝑀(e.g.,100possibleflightmissions)andflightsegment𝑆(e.g.,15possibleflightsegments)thecolumnentriesofthematrixaregivenbythefollowingvector,

𝚩 𝑖, : =

𝑅 𝑛𝑚𝑖ℎ 𝑓𝑡

𝑉!"# 𝑘𝑛𝑡𝑠𝑀 −𝐶! −𝐶!𝐶!

−

𝑊𝑀𝑇𝑂𝑊 −

𝐹!"# 𝑘𝑁𝑚! 𝑘𝑔 𝑠𝑒𝑐!!

𝐴𝑛𝑔𝑙𝑒 𝑑𝑒𝑔𝑇! [𝐾]𝑃![𝑃𝑎]

!

. Eq.8

For example, 𝚩(𝑀 ∙ 15+ 𝑆, : ) represents the aircraft performance at mission𝑀 and flightsegment 𝑆. The first 50 missions are flown under ISA conditions (e.g., 𝑇!,!" = 0) and theremaining50missionsareflownundernon-ISAconditions(e.g.,𝑇!,!" ≠ 0).

The AEDT inputs are the SQL FLEET database tables given in Table 15. The objective is todeterminetheappropriatecoefficient intheSQLFLEETdatabasetablesthatwouldaccuratelyrepresenttheaircraftflightperformancecomputedbyTASOpt.UsingtheseSQLFLEETdatabasetables, a usermay import this information into AEDT and fly an aircraft in AEDTwhichwasdesignedinTASOpt.Thenextsectionwilllookateachindividualtableandtransformthedatain𝚨and𝚩intothenecessarytableentries.

34

TransformationThe following section presets the transformation from TASOpt output to AEDT input. Thediscussion assumes FLEET_ID is 60000, BADA_ID is ‘ZZ000’, and the SQL database name isFLEET.ThesectionwillfirstintroduceeachAEDTtablealongwiththedescriptionoftheAEDTtablefollowedbyaTASOpttransformationtabledescribingthevariablesintheAEDTtable.Thetransformationswereobtainedusingengineering judgmentwhileattemptingtoduplicatetheAEDTBoeing737-800aircraftcoefficientsfromTASOptflightperformanceoutputs.

FLT_FLEET

UPDATE[FLEET].[dbo].[FLT_FLEET]SET[MAX_TAKEOFF_WGT] =Var1,[MAX_LANDING_WGT] =Var2,[ENG_PRESSURE_RATIO] =Var3,[ENG_MAX_RATED_THRUST] =Var4,[AEDT_OPERATING_EMPTY_WEIGHT_LBS] =Var5,[MAX_PAYLOAD] =Var6,[FUEL_CAPACITY_US_GALS_FLOAT] =Var7WHERE[FLEET_ID]=60000

Name Description Unit TASOptVar1 MTOW [kg] 𝚨(1) ∙lb_kgVar2 MaxLandingWeight [kg] (𝚨 1 − 𝚨 3 ∙ 0.85) ∙lb_kgVar3 OPR [-] RandomVariableVar4 EngineMaxThrust [kN] 𝚨(5)Var5 EmptyWeight [kg] 𝚨(2)Var6 MaxPayload [kg] 215 ∙ 180 = 38,700 ∙ lb_kgVar7 FuelCapacity [gal] 𝚨(3) ∙𝜌!"#$

ThefuelforthisstudyisKerosenewhichhasaweightof6.75[lb]pergallon,𝜌!"#$ = 1/6.75.

35

FLT_BADA_THRUST

UPDATE[FLEET].[dbo].[FLT_BADA_THRUST]SET[COEFF_TC1] = 𝑻𝑪𝑪𝟏, [COEFF_TC2] = 𝑻𝑪𝑪𝟐,[COEFF_TC3] = 𝑻𝑪𝑪𝟑, [COEFF_TC4] = 𝑻𝑪𝑪𝟒,[COEFF_TC5] = 𝑻𝑪𝑪𝟓, [COEFF_TDL] = 𝑻𝑪𝑫,𝑳𝑶,[COEFF_TDH] = 𝑻𝑪𝑫,𝑯𝑰, [DES_ALT] = 𝒉𝑫𝑬𝑺,[COEFF_TAPP] = 𝑻𝑪𝑨𝑷𝑷, [COEFF_TLD] = 𝑻𝑪𝑳𝑫,[DES_CAS] = 𝑽𝑫,𝑪𝑨𝑺, [DES_MACH] = 𝑴𝑫𝑬𝑺WHERE[BADA_ID]='ZZ000'

AEDT(3.6.3.14)Themaximumtotalnetthrust[N]duringclimbinISAconditionsisgivenby:

𝐹!,!!"# = 𝑇𝐶!! ∙ 1−ℎ

𝑇𝐶!!+ 𝑇𝐶!! ∙ ℎ! Eq.9

where

ℎ aircraftaltitudeabovemeansealevel[ft]𝑇𝐶!! 1stmaxclimbthrustcoefficient[N]𝑇𝐶!! 2ndmaxclimbthrustcoefficient[ft]𝑇𝐶!! 3rdmaxclimbthrustcoefficient[ft2]

TASOptAEDTmaximumnetthrustistotalaircraftthrustwhereasTASOptenginethrustoutputisperengine,thereforetheTASOptenginethrustmustbemultipliedbynumberofengines.

Mission Segment AEDT TASOpt[1:50] [5:8] 𝐹!,!!"# 𝐁(𝑀 ∗ 15+ 𝑆, 8) ∙ 𝑛!"# ∙ 𝑁_𝑘𝑁[1:50] [5:8] ℎ 𝐁(𝑀 ∗ 15+ 𝑆,2)

AEDT(3.6.3.14)Themaximumtotalnetthrust[N]duringclimbforallweathercontextsisgivenby:

𝐹!" = 𝐹!,!!"# ∙ 1− 𝑇𝐶!! ∙ ∆𝑇!"!!""

Eq.10

with

∆𝑇!"!!"" = ∆𝑇!"# − 𝑇𝐶!!

36

andthelimitationsthat

0.0 ≤ 𝑇𝐶!! ∙ ∆𝑇!"!!"" ≤ 0.4and

𝑇𝐶!! ≥ 0.0

where

∆𝑇!"# AtmospherictemperaturedeviationfromISA[K]𝑇𝐶!! 4ththrusttemperaturecoefficient[K]𝑇𝐶!! 5ththrusttemperaturecoefficient[K-1]

TASOpt

Mission Segment AEDT TASOpt[51:100] [2:7] 𝐹!" 𝐁(𝑀 ∗ 15+ 𝑆, 8) ∙ 𝑛!"# ∙ 𝑁_𝑘𝑁[51:100] [2:7] ∆𝑇!"# 𝐁 𝑀 ∗ 15+ 𝑆, 10 − 𝑇!"# ℎ [51:100] [2:7] 𝑇𝐶!! max (𝑇𝐶!!, 0)

AEDT(3.6.3.14)Thestandardtotalnetthrust[N]duringdescentisgivenby:

𝐹!" = 𝑇𝐶!,!" ∙ 𝐹!" ℎ > ℎ!"#𝑇𝐶!,!" ∙ 𝐹!" ℎ ≤ ℎ!"#

Eq.11

𝐹!" = 𝑇𝐶!"" ∙ 𝐹!" ℎ ≤ 1000 𝑓𝑡 Eq.12𝐹!" = 𝑇𝐶!" ∙ 𝐹!" ℎ ≤ 100 𝑓𝑡 Eq.13

𝑀!"# Eq.14 𝑉!,!"# Eq.15

where

ℎ!"# Transitionaltitudeforcalculationofdescentthrust[ft]𝑇𝐶!,!" Highaltitudedescentthrustcoefficient[-]𝑇𝐶!,!" Lowaltitudedescentthrustcoefficient[-]𝑇𝐶!"" Approachthrustcoefficient[-]𝑇𝐶!" Landingthrustcoefficient[-]𝑀!" DescentMachNumber[-]𝑉!,!"# DescentCalibratedAirspeed[kt]

Airdensityandcalibratedairspeedarecomputedasfollows,

37

𝜌 ℎ =𝛾 ∙ 𝑃 ℎ

𝛾 − 1 ∙ 𝐶! ∙ 𝑇 ℎ Eq.16

𝑉!"# =2 ∙ 𝑃!"#,!𝛾 − 1𝛾 ∙ 𝜌

∙ 1+𝑃 ℎ𝑃!"#,!

∙ 1+𝛾 − 1𝛾 ∙

𝜌 ℎ ∙ 𝑉!"#!

2 ∙ 𝑃! ℎ

!!

!

− 1 Eq.17

where𝑃!"#,! = 101.325 [𝑘𝑃𝐴],𝛾 = 1.4,and𝐶! = 1004.0.

TASOpt

Mission Segment AEDT TASOpt[1:100] [14] ℎ!"# 𝔼! 𝔼! 𝐁 : ,2 [1:100] [11:14] 𝑀!"# 𝔼! 𝔼! 𝐁 : ,4 [1:100] [12:14] 𝑉!,!"# 𝔼! 𝔼! 𝑉!"# ∙ 𝑘𝑡_𝑚𝑠!![1:100] [12:13] 𝐹!" 𝑇𝐶!,!" 𝐁 𝑀 ∗ 15+ 𝑆, 8 ∙ 𝑛!"# ∙ 𝑁_𝑘𝑁[1:100] [14] 𝐹!" 𝑇𝐶!,!" 𝐁 𝑀 ∗ 15+ 𝑆, 8 ∙ 𝑛!"# ∙ 𝑁_𝑘𝑁[1:100] [15] 𝐹!" 𝑇𝐶!"" 𝐁 𝑀 ∗ 15+ 𝑆, 8 ∙ 𝑛!"# ∙ 𝑁_𝑘𝑁[1:100] [15] 𝐹!" 𝑇𝐶!" 𝐁 𝑀 ∗ 15+ 𝑆, 8 ∙ 𝑛!"# ∙ 𝑁_𝑘𝑁

FLT_BADA_ACFT

UPDATE[FLEET].[dbo].[FLT_BADA_ACFT]SET[MASS_REF] = 𝑴𝒓𝒆𝒇, [MASS_MIN] =𝑴𝒎𝒊𝒏,[MASS_MAX] = 𝑴𝒎𝒂𝒙, [MASS_PAYLD] =𝑴𝒑𝒂𝒚,[MASS_GRAD] = 𝑮𝒘, [FENV_VMO] =𝑽𝑴𝑶,[FENV_MMO] = 𝑴𝑴𝑶, [FENV_ALT] =𝒉𝑴𝑶,[FENV_HMAX] = 𝒉𝒎𝒂𝒙, [FENV_TEMP] =𝑮𝒕,[WING_AREA] = 𝑨 𝟒 , [COEFF_CLBO] =𝑪𝑳𝒃𝒐 𝑴!𝟎 ,[BUFF_GRAD] =𝒌, [COEFF_CM16]=0,[NUM_ENGS] =𝒏𝒆𝒏𝒈WHERE[BADA_ID]='ZZ001'

38

AEDT

𝑀!"# ReferenceAircraftMass𝑀!"# MinimumAircraftMass𝑀!"# MaximumAircraftMass𝑀!"# MaximumPayloadMass𝑉!" MaximumOperationalSpeed𝑀!" MaximumOperationalMachNumberℎ!" Maximumoperationalheightabovesealevelℎ!"# MaximumaltitudeatMTOWunderISAconditionsformaxmass

TASOpt

Mission Segment AEDT TASOpt[1:100] [1:15] 𝑀!"# 𝑨(1) ∙ 𝔼! 𝔼! 𝐁 𝑀 ∗ 15+ 𝑆, 7 ∙ 𝑙𝑏_𝑡𝑜𝑛

- - 𝑀!"# 𝑨(2) ∙ 𝑙𝑏_𝑡𝑜𝑛- - 𝑀!"# 𝑨(1) ∙ 𝑙𝑏_𝑡𝑜𝑛- - 𝑀!"# 215 ∙ 180 = 37,800∙ 𝑙𝑏_𝑡𝑜𝑛

[1:100] [1:15] 𝑉!" 𝑚𝑎𝑥! 𝑚𝑎𝑥! V!"# ∙ 𝑘𝑡_𝑚𝑠!![1:100] [1:15] 𝑀!" 𝑚𝑎𝑥! 𝑚𝑎𝑥! 𝐁 𝑀 ∗ 15+ 𝑆, 4 [1:100] [1:15] ℎ!" 𝑚𝑎𝑥! 𝑚𝑎𝑥! 𝐁 𝑀 ∗ 15+ 𝑆, 2 [1] [9] ℎ!"# 𝐁 𝑀 ∗ 15+ 𝑆, 2

AEDT:3.6.3.1.5Themaximumaltitudeachievablebytheaircraftℎ![ft]isgivenby:

ℎ! = min ℎ!" , ℎ!"# + ∆𝑇!"# − 𝐶!!! ∙ 𝐺! + 𝑚!"# −𝑚 ∙ 𝐺! Eq.18

where

𝐺! Massgradientonmaximumaltitude[ft]𝐺! Temperaturegradientonmaximumaltitude[ftK-1]𝑚 Aircraftmass[kg]

𝑚!"# MaximumMass[kg]

39

TASOpt

Mission Segment AEDT TASOpt- - 𝑚!"# 𝐀(1) ∙ 𝑙𝑏_𝑘𝑔

[1:100] [8:10] 𝑚 𝐀(1) ∙ 𝐁 𝑀 ∗ 15+ 𝑆, 7 ∙ 𝑙𝑏_𝑘𝑔[1:100] [8:10] ∆𝑇!"# 𝐁 𝑀 ∗ 15+ 𝑆, 10 − 𝑇!"# ℎ

BADA:3.6.2(BADATech.Manual)Forjetaircraftalowspeedbuffetinglimithasbeenintroduced.ThisbuffetinglimitisexpressedasaMachnumberandcanbedeterminedusingthefollowingequation:

𝑘 ∙𝑀! − 𝐶!"# !!! ∙𝑀! +𝑊

𝑆 ∙ 𝑝 ∙ 0.583 = 0 Eq.19

where

𝑘 Liftcoefficientgradient𝐶!"# !!! Initialbuffetonsetliftcoefficientfor𝑀 = 0

𝑝 Actualpressure[Pa]𝑀 MachNumber𝑆 WingReferenceArea 𝑚! 𝑊 AircraftWeight[N]

TASOpt

Mission Segment AEDT TASOpt[1:100] [34] 𝑊 𝐀(1) ∙ 𝐁 𝑀 ∗ 15+ 𝑆, 7 ∙ 𝑙𝑏_𝑁[1:100] [34] 𝑀 𝐁 𝑀 ∗ 15+ 𝑆, 4

- - 𝑆 𝐀 4 ∙ 𝑓𝑡!_𝑚![1:100] [34] 𝑝 𝐁 𝑀 ∗ 15+ 𝑆, 11

40

FLT_BADA_CONFIG

UPDATE[FLEET].[dbo].[FLT_BADA_CONFIG]SET[VSTALL]=𝑽𝒔𝒕𝒂𝒍𝒍𝑨𝑷, [COEFF_CD0]=𝑪𝑫𝟎,𝑨𝑷, [COEFF_CD2]=𝑪𝑫𝟐,𝑨𝑷WHERE[BADA_ID]='ZZ001'AND[PHASE]='AP'UPDATE[FLEET].[dbo].[FLT_BADA_CONFIG]SET[VSTALL]=𝑽𝒔𝒕𝒂𝒍𝒍𝑪𝑹, [COEFF_CD0]=𝑪𝑫𝟎,𝑪𝑹, [COEFF_CD2]=𝑪𝑫𝟐,𝑪𝑹WHERE[BADA_ID]='ZZ001'AND[PHASE]='CR'UPDATE[FLEET].[dbo].[FLT_BADA_CONFIG]SET[VSTALL]=𝑽𝒔𝒕𝒂𝒍𝒍𝑰𝑪, [COEFF_CD0]=𝑪𝑫𝟎,𝑰𝑪, [COEFF_CD2]=𝑪𝑫𝟐,𝑰𝑪WHERE[BADA_ID]='ZZ001'AND[PHASE]='IC'UPDATE[FLEET].[dbo].[FLT_BADA_CONFIG]SET[VSTALL]=𝑽𝒔𝒕𝒂𝒍𝒍𝑳𝑫, [COEFF_CD0]=𝑪𝑫𝟎,𝑳𝑫, [COEFF_CD2]=𝑪𝑫𝟐,𝑳𝑫WHERE[BADA_ID]='ZZ001'AND[PHASE]='LD'UPDATE[FLEET].[dbo].[FLT_BADA_CONFIG]SET[VSTALL]=𝑽𝒔𝒕𝒂𝒍𝒍𝑻𝑶, [COEFF_CD0]=𝑪𝑫𝟎,𝑻𝑶, [COEFF_CD2]=𝑪𝑫𝟐,𝑻𝑶WHERE[BADA_ID]='ZZ001'AND[PHASE]='TO'

AEDT:3.6.3.1.3CoefficientofDragCD(N)iscalculatedfrom:

𝐶! = 𝐶!!,! + 𝐶!!,! ∙𝑊

12 ∙ 𝜌 ∙ 𝑆 ∙ 𝑉!"#

!

!

= 𝐶!!,! + 𝐶!!,! ∙ 𝐶! ! Eq.20

where

𝐶!!,! Parasiticdragcoefficientin𝑋condifiguration[-]𝐶!!,! Induceddragcoefficientin𝑋condifiguration[-]𝐶! CoefficientofLift[-]𝜌 AtmosphericDensity[kgm-3]𝑉!"# AircraftTrueAirspeed[ms-1]𝑆 WingReferenceArea 𝑚! 𝑊 AircraftWeight[N]

41

TASOpt

Mission Segment AEDT TASOpt[1:100] [23] 𝐶! 𝑋 = 𝑇𝑂 𝐁 𝑀 ∗ 15+ 𝑆, 6 /𝐁 𝑀 ∗ 15+ 𝑆, 5 [1:100] [23] 𝐶! 𝑋 = 𝑇𝑂 𝐁 𝑀 ∗ 15+ 𝑆, 5 [1:100] [4:7] 𝐶! 𝑋 = 𝐶𝐿 𝐁 𝑀 ∗ 15+ 𝑆, 6 /𝐁 𝑀 ∗ 15+ 𝑆, 5 [1:100] [4:7] 𝐶! 𝑋 = 𝐶𝐿 𝐁 𝑀 ∗ 15+ 𝑆, 5 [1:100] [910] 𝐶! 𝑋 = 𝐶𝑅 𝐁 𝑀 ∗ 15+ 𝑆, 6 /𝐁 𝑀 ∗ 15+ 𝑆, 5 [1:100] [910] 𝐶! 𝑋 = 𝐶𝑅 𝐁 𝑀 ∗ 15+ 𝑆, 5 [1:100] [12:13] 𝐶! 𝑋 = 𝐴𝑃 𝐁 𝑀 ∗ 15+ 𝑆, 6 /𝐁 𝑀 ∗ 15+ 𝑆, 5 [1:100] [12:13] 𝐶! 𝑋 = 𝐴𝑃 𝐁 𝑀 ∗ 15+ 𝑆, 5 [1:100] [15] 𝐶! 𝑋 = 𝐿𝐷 𝐁 𝑀 ∗ 15+ 𝑆, 6 /𝐁 𝑀 ∗ 15+ 𝑆, 5 [1:100] [15] 𝐶! 𝑋 = 𝐿𝐷 𝐁 𝑀 ∗ 15+ 𝑆, 5

BADA:3.5b(BADATech.Manual)Theminimumcalibratedairspeedin 𝑋configurationiscalculatedfrom

𝑉!"#! = 𝐶!!"# ∙ 𝑉!"#$!! Eq.21where

𝐶!!"# Minimumspeedcoefficientinnon-take-offconfiguration[-]𝑉!"#$!! Aircraft’sstallcalibratedairspeedin𝑋configuration[kt]

wherethestallspeediscomputeas

𝑉!"#,!"#$$ =2 ∙𝑊

𝜌 ∙ 𝑆 ∙ 𝐶!,!"# Eq.22

TASOpt

Mission Segment AEDT TASOpt[1:100] [2] 𝑉!"#$!! 𝑋 = 𝑇𝑂 Eq.22[1:100] [4] 𝑉!"#$!! 𝑋 = 𝐼𝐶 Eq.22[1:100] [910] 𝑉!"#$!! 𝑋 = 𝐶𝑅 Eq.22[1:100] [14] 𝑉!"#$!! 𝑋 = 𝐴𝑃 Eq.22[1:100] [15] 𝑉!"#$!! 𝑋 = 𝐿𝐷 Eq.22

42

FLT_BADA_FUEL

UPDATE[FLEET].[dbo].[FLT_BADA_FUEL]SET[COEFF_CF1] =𝑪𝒇𝟏,[COEFF_CF2] =𝑪𝒇𝟐,[COEFF_CF3] = 𝑪𝒇𝟑, [COEFF_CF4] =𝑪𝒇𝟒, [COEFF_CFCR]=𝑪𝒇𝑪𝑹 WHERE[BADA_ID]='ZZ001'

AEDT:3.4.1The nominal total rate of fuel flow𝑓!"# [kgmin-1] for an aircraft,which is applicable for allsituationswhere the aircraft is neither in the cruise phase of flight nor operating at an idlethrustsetting,isgivenby:

𝑓!"# = 1+𝑉!"#𝐶!!

∙ 𝐶!! ∙ 𝐹 Eq.23

where

𝐹 Aircrafttotalnetthrustfromitsengine[nK]𝐶!! Aircraft-specific1stthrustspecificfuelconsumptioncoefficient[kgmin-1kN-1]𝐶!! Aircraft-specific2ndthrustspecificfuelconsumptioncoefficient[kt]

TASOpt

Mission Segment AEDT TASOpt[1:100] [4:8] 𝑓!"# 𝐁 𝑀 ∗ 15+ 𝑆, 9 ∙𝑚𝑖𝑛_𝑠𝑒𝑐[1:100] [4:8] 𝐹 𝐁 𝑀 ∗ 15+ 𝑆, 8 ∙ 𝑛!"#[1:100] [4:8] 𝑉!"# 𝐁 𝑀 ∗ 15+ 𝑆, 3 ∙ 𝑘𝑡_𝑚𝑠!!

AEDT:3.4.1TheBADAtotalfuelflowrate𝑓!"#[kgmin-1]foranaircraftinanidlestateisgivenby:

𝑓!"# = 1−ℎ𝐶!!

∙ 𝐶!! Eq.24

where

𝐶!! Aircraft-specific1stdescentfuelflowcoefficient[kgmin-1]𝐶!! Aircraft-specific2nddescentfuelflowcoefficient[ft]ℎ AltitudeaboveMSL[ft]

43

TASOpt

Mission Segment AEDT TASOpt[1:100] [11:14] 𝑓!"# 𝐁 𝑀 ∗ 15+ 𝑆, 9 ∙𝑚𝑖𝑛_𝑠𝑒𝑐[1:100] [11:14] ℎ 𝐁 𝑀 ∗ 15+ 𝑆, 2

AEDT:3.4.1The BADA total fuel flow rate𝑓!" [kgmin-1] for an aircraft in a cruise state is calculated byscalingthenominalflowrate:

𝑓!" = 𝐶!!" ∙ 𝑓!"# Eq.25where

𝐶!!" Aircraft-specificcruiseflueflowcorrectioncoefficient[-]

TASOpt

Mission Segment AEDT TASOpt[1:100] [9:10] 𝑓!" 𝐁 𝑀 ∗ 15+ 𝑆, 9 ∙𝑚𝑖𝑛_𝑠𝑒𝑐

FLT_BADA_APF

UPDATE[FLEET].[dbo].[FLT_BADA_APF]SET[CL_CAS_1]=𝑽𝒄𝒍,𝟏,𝑨𝑽, [CL_CAS_2]=𝑽𝒄𝒍,𝟐,𝑨𝑽, [CL_MACH]=𝑴𝒄𝒍,𝑨𝑽,[CR_CAS_1]=𝑽𝒄𝒓,𝟏,𝑨𝑽, [CR_CAS_2]=𝑽𝒄𝒓,𝟐,𝑨𝑽, [CR_MACH]=𝑴𝒄𝒓,𝑨𝑽,[DE_CAS_1]=𝑽𝒅𝒆,𝟏,𝑨𝑽, [DE_CAS_2]=𝑽𝒅𝒆,𝟐,𝑨𝑽, [DE_MACH]=𝑴𝒅𝒆,𝑨𝑽WHERE[BADA_ID]='ZZ001'AND[MASS_RANGE]='AV'UPDATE[FLEET].[dbo].[FLT_BADA_APF]SET[CL_CAS_1]=𝑽𝒄𝒍,𝟏,𝑯𝑰, [CL_CAS_2]=𝑽𝒄𝒍,𝟐,𝑯𝑰, [CL_MACH]=𝑴𝒄𝒍,𝑯𝑰,[CR_CAS_1]=𝑽𝒄𝒓,𝟏,𝑯𝑰, [CR_CAS_2]=𝑽𝒄𝒓,𝟐,𝑯𝑰, [CR_MACH]=𝑴𝒄𝒓,𝑯𝑰,[DE_CAS_1]=𝑽𝒅𝒆,𝟏,𝑯𝑰, [DE_CAS_2]=𝑽𝒅𝒆,𝟐,𝑯𝑰, [DE_MACH]=𝑴𝒅𝒆,𝑯𝑰WHERE[BADA_ID]='ZZ001'AND[MASS_RANGE]='HI'UPDATE[FLEET].[dbo].[FLT_BADA_APF]SET[CL_CAS_1]=𝑽𝒄𝒍,𝟏,𝑳𝑶, [CL_CAS_2]=𝑽𝒄𝒍,𝟐,𝑳𝑶, [CL_MACH]=𝑴𝒄𝒍,𝑳𝑶,[CR_CAS_1]=𝑽𝒄𝒓,𝟏,𝑳𝑶, [CR_CAS_2]=𝑽𝒄𝒓,𝟐,𝑳𝑶, [CR_MACH]=𝑴𝒄𝒓,𝑳𝑶,[DE_CAS_1]=𝑽𝒅𝒆,𝟏,𝑳𝑶, [DE_CAS_2]=𝑽𝒅𝒆,𝟐,𝑳𝑶, [DE_MACH]=𝑴𝒅𝒆,𝑳𝑶WHERE[BADA_ID]='ZZ001'AND[MASS_RANGE]='LO'

44

BADA:4(BADATech.Manual)Thefollowingparametersaredefinedforeachaircrafttypetocharacterizetheclimbphase:

𝑉!",! = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐶𝑙𝑖𝑚𝑏 𝐶𝐴𝑆 𝑘𝑡 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 1,500/6,000 𝑓𝑡 𝑎𝑛𝑑 10,000 [𝑓𝑡] Eq.26𝑉!",! = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐶𝑙𝑖𝑚𝑏 𝐶𝐴𝑆 𝑘𝑡 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 10,000 𝑓𝑡 𝑎𝑛𝑑 𝑀𝑎𝑐ℎ 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 Eq.27𝑀!" = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑐𝑙𝑖𝑚𝑏 𝑀𝑎𝑐ℎ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑎𝑏𝑜𝑣𝑒 𝑀𝑎𝑐ℎ 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 Eq.28

where

𝐴𝑉 Averagemissionflightrange𝐻𝐼 Highmissionflightrange𝐿𝑂 Lowmissionflightrange

TASOpt

Mission Segment AEDT TASOpt[1:100] [4:8] 𝐿𝑂! 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐿𝑂

𝐁 𝑀 ∗ 15 + 𝑆, 2 < 10,000 [𝑓𝑡]

[1:100] [4:8] 𝐿𝑂! 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐿𝑂 𝐁 𝑀 ∗ 15 + 𝑆, 2 > 10,000 [𝑓𝑡]

[1:100] [4:8] 𝑉!",! 𝐿𝑂 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐿𝑂! ∙ 𝑘𝑡_𝑚𝑠!![1:100] [4:8] 𝑉!",! 𝐿𝑂 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐿𝑂! ∙ 𝑘𝑡_𝑚𝑠!![1:100] [4:8] 𝑀!" 𝐿𝑂 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 4 [1:100] [4:8] 𝐴𝑉! 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐴𝑉

𝐁 𝑀 ∗ 15 + 𝑆, 2 < 10,000 [𝑓𝑡]

[1:100] [4:8] 𝐴𝑉! 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐴𝑉 𝐁 𝑀 ∗ 15 + 𝑆, 2 > 10,000 [𝑓𝑡]

[1:100] [4:8] 𝑉!",! 𝐴𝑉 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐴𝑉! ∙ 𝑘𝑡_𝑚𝑠!![1:100] [4:8] 𝑉!",! 𝐴𝑉 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐴𝑉! ∙ 𝑘𝑡_𝑚𝑠!![1:100] [4:8] 𝑀!" 𝐴𝑉 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 4 [1:100] [4:8] 𝐻𝐼! 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐻𝐼

𝐁 𝑀 ∗ 15 + 𝑆, 2 < 10,000 [𝑓𝑡]

[1:100] [4:8] 𝐻𝐼! 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐻𝐼 𝐁 𝑀 ∗ 15 + 𝑆, 2 > 10,000 [𝑓𝑡]

[1:100] [4:8] 𝑉!",! 𝐻𝐼 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐻𝐼! ∙ 𝑘𝑡_𝑚𝑠!![1:100] [4:8] 𝑉!",! 𝐻𝐼 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐻𝐼! ∙ 𝑘𝑡_𝑚𝑠!![1:100] [4:8] 𝑀!" 𝐻𝐼 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 4

45

BADA:4(BADATech.Manual)Thefollowingparametersaredefinedforeachaircrafttypetocharacterizethedescentphase:

𝑉!",! = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑠𝑐𝑒𝑛𝑡 𝐶𝐴𝑆 𝑘𝑡 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 1,500/6,000 𝑓𝑡 𝑎𝑛𝑑 10,000 [𝑓𝑡] Eq.29𝑉!",! = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑠𝑐𝑒𝑛𝑡 𝐶𝐴𝑆 𝑘𝑡 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 10,000 𝑓𝑡 𝑎𝑛𝑑 𝑀𝑎𝑐ℎ 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 Eq.30𝑀!" = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑠𝑐𝑒𝑛𝑡 𝑀𝑎𝑐ℎ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑎𝑏𝑜𝑣𝑒 𝑀𝑎𝑐ℎ 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 Eq.31

where

𝐴𝑉 Averagemissionflightrange𝐻𝐼 Highmissionflightrange𝐿𝑂 Lowmissionflightrange

TASOpt

Mission Segment AEDT TASOpt[1:100] [11:15] 𝐿𝑂! 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐿𝑂

𝐁 𝑀 ∗ 15 + 𝑆, 2 < 10,000 [𝑓𝑡]

[1:100] [11:15] 𝐿𝑂! 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐿𝑂 𝐁 𝑀 ∗ 15 + 𝑆, 2 > 10,000 [𝑓𝑡]

[1:100] [11:15] 𝑉!",! 𝐿𝑂 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐿𝑂! ∙ 𝑘𝑡_𝑚𝑠!![1:100] [11:15] 𝑉!",! 𝐿𝑂 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐿𝑂! ∙ 𝑘𝑡_𝑚𝑠!![1:100] [11:15] 𝑀!" 𝐿𝑂 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 4 [1:100] [11:15] 𝐴𝑉! 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐴𝑉

𝐁 𝑀 ∗ 15 + 𝑆, 2 < 10,000 [𝑓𝑡]

[1:100] [11:15] 𝐴𝑉! 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐴𝑉 𝐁 𝑀 ∗ 15 + 𝑆, 2 > 10,000 [𝑓𝑡]

[1:100] [11:15] 𝑉!",! 𝐴𝑉 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐴𝑉! ∙ 𝑘𝑡_𝑚𝑠!![1:100] [11:15] 𝑉!",! 𝐴𝑉 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐴𝑉! ∙ 𝑘𝑡_𝑚𝑠!![1:100] [11:15] 𝑀!" 𝐴𝑉 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 4 [1:100] [11:15] 𝐻𝐼! 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐻𝐼

𝐁 𝑀 ∗ 15 + 𝑆, 2 < 10,000 [𝑓𝑡]

[1:100] [11:15] 𝐻𝐼! 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐻𝐼 𝐁 𝑀 ∗ 15 + 𝑆, 2 > 10,000 [𝑓𝑡]

[1:100] [11:15] 𝑉!",! 𝐻𝐼 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐻𝐼! ∙ 𝑘𝑡_𝑚𝑠!![1:100] [11:15] 𝑉!",! 𝐻𝐼 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐻𝐼! ∙ 𝑘𝑡_𝑚𝑠!![1:100] [11:15] 𝑀!" 𝐻𝐼 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 4

46

BADA:4(BADATech.Manual)Thefollowingparametersaredefinedforeachaircrafttypetocharacterizethecruisephase:

𝑉!",! = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑐𝑟𝑢𝑖𝑠𝑒 𝐶𝐴𝑆 𝑘𝑡 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 1,500/6,000 𝑓𝑡 𝑎𝑛𝑑 10,000 [𝑓𝑡] Eq.32𝑉!",! = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑐𝑟𝑢𝑖𝑠𝑒 𝐶𝐴𝑆 𝑘𝑡 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 10,000 𝑓𝑡 𝑎𝑛𝑑 𝑀𝑎𝑐ℎ 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 Eq.33𝑀!" = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑐𝑟𝑢𝑖𝑠𝑒 𝑀𝑎𝑐ℎ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑎𝑏𝑜𝑣𝑒 𝑀𝑎𝑐ℎ 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 Eq.34

where

𝐴𝑉 Averagemissionflightrange𝐻𝐼 Highmissionflightrange𝐿𝑂 Lowmissionflightrange

TASOpt

Mission Segment AEDT TASOpt[1:100] [910] 𝐿𝑂 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐿𝑂

𝐁 𝑀 ∗ 15 + 𝑆, 2 > 10,000 [𝑓𝑡]

[1:100] [910] 𝑉!",! 𝐿𝑂 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐿𝑂 ∙ 𝑘𝑡_𝑚𝑠!![1:100] [910] 𝑉!",! 𝐿𝑂 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐿𝑂 ∙ 𝑘𝑡_𝑚𝑠!![1:100] [910] 𝑀!" 𝐿𝑂 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 4 [1:100] [910] 𝐴𝑉 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐴𝑉

𝐁 𝑀 ∗ 15 + 𝑆, 2 > 10,000 [𝑓𝑡]

[1:100] [910] 𝑉!",! 𝐴𝑉 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐴𝑉 ∙ 𝑘𝑡_𝑚𝑠!![1:100] [910] 𝑉!",! 𝐴𝑉 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐴𝑉 ∙ 𝑘𝑡_𝑚𝑠!![1:100] [910] 𝑀!" 𝐴𝑉 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 4 [1:100] [910] 𝐻𝐼 𝐁 𝑀 ∗ 15 + 𝑆, 1 = 𝐻𝐼

𝐁 𝑀 ∗ 15 + 𝑆, 2 > 10,000 [𝑓𝑡]

[1:100] [910] 𝑉!",! 𝐻𝐼 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐻𝐼 ∙ 𝑘𝑡_𝑚𝑠!![1:100] [910] 𝑉!",! 𝐻𝐼 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 3 𝐻𝐼 ∙ 𝑘𝑡_𝑚𝑠!![1:100] [910] 𝑀!" 𝐻𝐼 𝔼! 𝔼! 𝐁 𝑀 ∗ 15 + 𝑆, 4

FLT_ANP_AIRPLANES

UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANES]SET[MX_GW_TKO] =Var1, [MX_GW_LND] =Var2,[THR_STATIC] =Var3, [MIN_BURN] =Var4,[NUMB_ENG] =𝒏𝒆𝒏𝒈WHERE[ACFT_ID]='MIT1'

47

AEDT:Name Description Unit TASOptVar1 WMTO [lb] 𝐀(1)Var2 MaximumLandingWeight [lb] (𝐀 1 − 𝐀 3 ∙ 0.85)Var3 100%StaticThrust [lbf] 𝐀(5) ∙ 𝑘𝑁_𝑙𝑏𝑓Var4 MinimumFuelBurn [kgsec-1] 𝑚𝑎𝑥! 𝑚𝑎𝑥! 𝐁 𝑀 ∗ 15+ 𝑆, 9 ∙ 𝑙𝑏_𝑘𝑔/𝑛!"#

FLT_ANP_AIRPLANE_THRUST_JET

UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_THRUST_JET]SET[COEFF_E] = 𝑬𝒄𝒍𝒊𝒎𝒃, [COEFF_F] =𝑭𝒄𝒍𝒊𝒎𝒃, [COEFF_GA] = 𝑮𝑨𝒄𝒍𝒊𝒎𝒃,[COEFF_GB] = 𝑮𝑩𝒄𝒍𝒊𝒎𝒃, [COEFF_H] = 𝟎WHERE[ACFT_ID]='MIT1'AND[THRUST_TYPE]='C'UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_THRUST_JET]SET[COEFF_E] = 𝑬𝒕𝒂𝒌𝒆𝒐𝒇𝒇, [COEFF_F] =𝑭𝒕𝒂𝒌𝒆𝒐𝒇𝒇, [COEFF_GA] = 𝑮𝑨𝒕𝒂𝒌𝒆𝒐𝒇𝒇,[COEFF_GB] = 𝑮𝑩𝒕𝒂𝒌𝒆𝒐𝒇𝒇, [COEFF_H] = 𝟎WHERE[ACFT_ID]='MIT1'AND[THRUST_TYPE]='T'

AEDT:JetaircraftcorrectednetthrustperengineiscalculatedbyusingamodifiedversionofSAE-AIR-1845equation(A1):

𝐹!𝛿 = 𝐸 + 𝐹 ∙ 𝜐 + 𝐺! ∙ ℎ + 𝐺! ∙ ℎ! + 𝐻 ∙ 𝑇! Eq.35

where

𝐹!𝛿

Correctednetthrustperengine[lbf]

𝜐 Equivalent/calibratedairspeed[kt]ℎ Pressurealtitude[ft]MSL

𝑇! Temperature ℃ attheaircraft

𝐸,𝐹,𝐺!,𝐺! ,𝐻 Regressioncoefficientsthatdependonpowerstate(maxtakeoffandmaxclimb)andtemperaturestate(belowandaboveenginebreakpointtemperature)[lbf,lbf/kt,lbf/ft,lbf/ft2,lbf/℃]respectively

48

TASOpt

Mission Segment AEDT TASOpt[1:50] [4:7] 𝜐 Climb V!"#[1:50] [4:7] ℎ Climb 𝐁 𝑀 ∗ 15+ 𝑆, 2 [1:50] [4:7] 𝐹! Climb 𝐁 𝑀 ∗ 15+ 𝑆, 8 [1:50] [4:7] 𝛿 Climb 𝐁 𝑀 ∗ 15+ 𝑆, 12 /𝑃!"#(ℎ)[1:50] [2] 𝜐 Climb V!"#[1:50] [2] ℎ Climb 𝐁 𝑀 ∗ 15+ 𝑆, 2 [1:50] [2] 𝐹! Climb 𝐁 𝑀 ∗ 15+ 𝑆, 8 [1:50] [2] 𝛿 Climb 𝐁 𝑀 ∗ 15+ 𝑆, 12 /𝑃!"#(ℎ)

FLT_ANP_AIRPLANE_TSFC_COEFFICIENTS

UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_TSFC_COEFFICIENTS]SET[COEFF1] = 𝑪𝟏𝒂𝒓𝒓, [COEFF2] =𝑪𝟐𝒂𝒓𝒓,[COEFF3] =𝑪𝟑𝒂𝒓𝒓, [COEFF4] =𝑪𝟒𝒂𝒓𝒓 WHERE[ACFT_ID]='MIT1'AND[MODE]='A'UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_TSFC_COEFFICIENTS]SET[COEFF1] =𝑪𝟏𝒅𝒆𝒑, [COEFF2] =𝑪𝟐𝒅𝒆𝒑,[COEFF3] =𝑪𝟑𝒅𝒆𝒑, [COEFF4] =𝑪𝟒𝒅𝒆𝒑 WHERE[ACFT_ID]='MIT1'AND[MODE]='D'

AEDT(3.4.2):In the Senzig-Fleming-Lovinelli method, operation type and terminal area specific fuel burnmethods developed by the Volpe National Transportation System Center are used. For thismethod,fuelflowrateperengineduringdeparture𝑓!!"# [kgmin]iscalculatedas:

𝑓!!"#𝜃= 𝐹! ∙ 𝐶! + 𝐶! ∙𝑀 + 𝐶! ∙ ℎ!"# + 𝐶! ∙

𝐹!𝛿 Eq.36

where

𝐶! Aircraft-specific1stterminal-areadepartureTSFCcoefficient[kgmin-1kN-1]𝐶! Aircraft-specific2ndterminal-areadepartureTSFCcoefficient[kgmin-1kN-1]𝐶! Aircraft-specific3rdterminal-areadepartureTSFCcoefficient[kgmin-1kN-1]𝐶! Aircraft-specific3rdterminal-areadepartureTSFCcoefficient[kgmin-1kN-1]ℎ!"# AircraftaltitudewithrespecttoMSL[ft]𝑀 AircraftMachnumber[-]

49

𝜃 Ratiooftemperatureataircraftaltitudetosealleveltemperature[-]𝐹!/𝛿 Aircraftcorrectednetthrustperengine[lbf]𝐹! Aircraftnetthrustperengine[kN]

TASOpt

Mission Segment AEDT TASOpt[1:100] [4:8] 𝑓!!"# Depart 𝐁 𝑀 ∗ 15+ 𝑆, 9 [1:100] [4:8] 𝑀 Depart 𝐁 𝑀 ∗ 15+ 𝑆, 4 [1:100] [4:8] ℎ!"# Depart 𝐁 𝑀 ∗ 15+ 𝑆, 2 [1:100] [4:8] 𝐹! Depart 𝐁 𝑀 ∗ 15+ 𝑆, 8 [1:100] [4:8] 𝛿 Depart 𝐁 𝑀 ∗ 15+ 𝑆, 12 /𝑃![1:100] [4:8] 𝜃 Depart 𝐁 𝑀 ∗ 15+ 𝑆, 12 /𝑇!

AEDT:Fuelflowrateperengineduringapproach𝑓!!"" [kgmin-1]iscalculatedas:

𝑓!!""𝜃= 𝐹! ∙ 𝐶! + 𝐶! ∙𝑀 + 𝐶! ∙ 𝑒

−𝐶! ∙ 𝐹!/𝛿𝐹!!

Eq.37

where

𝐹!! ISAsea-levelstaticthrust[lbf]𝐶! Aircraft-specific1stterminal-areaarrivalTSFCcoefficient[kgmin-1kN-1]𝐶! Aircraft-specific2ndterminal-areaarrivalTSFCcoefficient[kgmin-1kN-1]𝐶! Aircraft-specific3rdterminal-areaarrivalTSFCcoefficient[kgmin-1kN-1]𝐶! Aircraft-specific3rdterminal-areaarrivalTSFCcoefficient[kgmin-1kN-1]𝑀 AircraftMachnumber[-]𝜃 Ratiooftemperatureataircraftaltitudetosealleveltemperature[-]

𝐹!/𝛿 Aircraftcorrectednetthrustperengine[lbf]𝐹! Aircraftnetthrustperengine[kN]

50

TASOpt

Mission Segment AEDT TASOpt[1:100] [11:14] 𝑓!!"" Arrival 𝐁 𝑀 ∗ 15+ 𝑆, 9 [1:100] [11:14] 𝑀 Arrival 𝐁 𝑀 ∗ 15+ 𝑆, 4 [1:100] [11:14] ℎ!"# Arrival 𝐁 𝑀 ∗ 15+ 𝑆, 2 [1:100] [11:14] 𝐹! Arrival 𝐁 𝑀 ∗ 15+ 𝑆, 8 [1:100] [11:14] 𝛿 Depart 𝐁 𝑀 ∗ 15+ 𝑆, 12 /𝑃![1:100] [11:14] 𝜃 Depart 𝐁 𝑀 ∗ 15+ 𝑆, 12 /𝑇!

FLT_ANP_AIRPLANE_FLAPS

UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_FLAPS]SET[COEFF_R] =𝑹𝒇,𝑺!𝟒, [COEFF_C_D] = 𝑪𝒅,𝑺!𝟒, [COEFF_B] = 𝑩𝒇,𝑺!𝟒WHERE[ACFT_ID]='MIT1'AND[FLAP_ID]='T_00'UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_FLAPS]SET[COEFF_R] =𝑹𝒇,𝑺!𝟑, [COEFF_C_D] = 𝑪𝒅,𝑺!𝟑, [COEFF_B] = 𝑩𝒇,𝑺!𝟑WHERE[ACFT_ID]='MIT1'AND[FLAP_ID]='T_01'UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_FLAPS]SET[COEFF_R] =𝑹𝒇,𝑺!𝟐, [COEFF_C_D] = 𝑪𝒅,𝑺!𝟐, [COEFF_B] = 𝑩𝒇,𝑺!𝟐WHERE[ACFT_ID]='MIT1'AND[FLAP_ID]='T_05'UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_FLAPS]SET[COEFF_R] =𝑹𝒇,𝑺!𝟏𝟒, [COEFF_C_D] =𝑪𝒅,𝑺!𝟏𝟒WHERE[ACFT_ID]='MIT1'AND[FLAP_ID]='A_40'UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_FLAPS]SET[COEFF_R] =𝑹𝒇,𝑺!𝟏𝟓, [COEFF_C_D] =𝑪𝒅,𝑺!𝟏𝟓WHERE[ACFT_ID]='MIT1'AND[FLAP_ID]='A_15'

AEDT(3.6.2.1.4.2):Thecalibratedairspeedattherotationpoint,whichisusedinthethrustequation,iscalculatedbyusingSAE-AIR-1845equation(A7):

𝑣! = 𝐶! ∙ 𝑊 Eq.38where

51

𝑣! Calibratedairspeed[kts]attakeoffrotation𝐶! Takeoffspeedcoefficientthatdependsonflapssetting[ktslbf-0.5]𝑊 Departureprofileweight[lbf];weightisassumedtoremainconstantforthe

entiredepartureprofile.

TASOpt

Mission Segment AEDT TASOpt[1:100] [2:4] 𝑣! Depart 𝑉!"#[1:100] [2:4] 𝑊 Depart 𝐀 1 ∙ 𝐁 𝑀 ∗ 15+ 𝑆, 7 [1:100] [2:4] 𝐶! Depart 𝔼! 𝑣!/𝑊

AEDT:Takeoffground-rolldistanceiscalculatedbyusingSAD-AIR-1845equation(A6):

𝑆! = 𝐵! ∙ 𝜃 ∙

𝑊𝛿

!

𝑁 ∙ 𝐹!𝛿 !

Eq.39

where

𝑆! Ground-rolldistance[ft]𝐵! Ground-rollcoefficient,whichdependsontheflapssetting[ftlbf-1]𝜃 Temperatureratioattheairportelevation[-]𝛿 Pressureratioattheairport[-]𝐹!𝛿 !

Correctednetthrustperengine[lbf]attakeoffrotation

wherethegroundrolldistanceis,

𝑆! = 1.21 ∙ 𝑊𝑆

𝜌 ∙ 𝐶! ∙𝐹! ∙ 𝑛!"#𝑊

. Eq.40

TASOpt

Mission Segment AEDT TASOpt[1:100] [2] 𝑆! Depart Eq.42

52

AEDT:TheaverageclimbangleiscalculatedbyusingSAE-AIR-1845equation(A8):

𝛾 = sin!! 𝐾 ∙ 𝑁 ∙ 𝐹!𝛿𝑊𝛿

− 𝑅! Eq.41

where

𝛾 Averageclimbangle[radians]𝐾 Speed-dependentconstant[-]

K=1.01whenclimbspeed≤200[kt];K=0.95otherwise.

𝑁 Numberofenginers[-]𝐹!𝛿 Nominalvalueofcorrectednetthrustperengine[lbf]

𝛿 Pressureratioattheairport[-]𝑊 Departureprofileweight[lbf]𝑅! Drag-over-liftcoefficientthatdependsontheflapsonthesetting[-]

TASOpt

Mission Segment AEDT TASOpt[1:100] [2] 𝛾 Depart1 𝐁 𝑀 ∗ 15+ 𝑆, 10 [1:100] [4] 𝛾 Depart2 𝐁 𝑀 ∗ 15+ 𝑆, 10 [1:100] [5] 𝛾 Depart3 𝐁 𝑀 ∗ 15+ 𝑆, 10

AEDT:𝑅!isusedtocalculatethethrustneeded,assumingaknownvaluefordescendangle𝛾.

𝐹!𝛿 !

=

𝑊𝛿!

∙ 𝑅! −𝑠𝑖𝑛 𝛾1.03

𝑁 Eq.42

where

𝐹!𝛿 !

Correctednetthrustperengine[lbf]ataltitude𝐴!

𝛾 Averagedescentangle(apositivevalue)

53

TASOpt

Mission Segment AEDT TASOpt[1:100] [14] 𝛾 Arrival15 𝐁 𝑀 ∗ 15+ 𝑆, 10 [1:100] [15] 𝛾 Arrival40 𝐁 𝑀 ∗ 15+ 𝑆, 10

AEDT:𝐷!isacoefficientusedbyAEDTtocalculatethelandingspeed.ForalandingsegmentinAEDTthefollowingequationisused:

𝐷! =𝑉!𝑊 Eq.43

where

𝑉! Calibratedairspeed[kt]justbeforelanding

TASOpt

Mission Segment AEDT TASOpt[1:100] [14] 𝑉! Arrival15 V!"#[1:100] [15] 𝑉! Arrival40 V!"#

FLT_ANP_AIRPLANE_PROFILES

UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_PROFILES]SET[WEIGHT]=𝑾𝑨WHERE[ACFT_ID]='MIT1'AND[OP_TYPE]='A'AND[PROF_ID1]='STANDARD'AND[PROF_ID2]=1UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_PROFILES]SET[WEIGHT]=𝑾𝟏,𝑫WHERE[ACFT_ID]='MIT1'AND[OP_TYPE]='D'AND[PROF_ID1]='STANDARD'AND[PROF_ID2]=1UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_PROFILES]SET[WEIGHT]=𝑾𝟐,𝑫WHERE[ACFT_ID]='MIT1'AND[OP_TYPE]='D'AND

54

[PROF_ID1]='STANDARD'AND[PROF_ID2]=2UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_PROFILES]SET[WEIGHT]=𝑾𝟑,𝑫WHERE[ACFT_ID]='MIT1'AND[OP_TYPE]='D'AND[PROF_ID1]='STANDARD'AND[PROF_ID2]=3UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_PROFILES]SET[WEIGHT]=𝑾𝟒,𝑫WHERE[ACFT_ID]='MIT1'AND[OP_TYPE]='D'AND[PROF_ID1]='STANDARD'AND[PROF_ID2]=4UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_PROFILES]SET[WEIGHT]=𝑾𝟓,𝑫WHERE[ACFT_ID]='MIT1'AND[OP_TYPE]='D'AND[PROF_ID1]='STANDARD'AND[PROF_ID2]=5UPDATE[FLEET].[dbo].[FLT_ANP_AIRPLANE_PROFILES]SET[WEIGHT]=𝑾𝟔,𝑫WHERE[ACFT_ID]='MIT1'AND[OP_TYPE]='D'AND[PROF_ID1]='STANDARD'AND[PROF_ID2]=6

AEDT:Theairplaneprofilesdefinetheaircraft’stakeoffweightwhichisafunctionofflightrange.Wewillassumeforaflightrangelessthan450[nmi]theaircraftweightis,

𝑊!"# =𝑊!"#$% +𝑊!"# , Eq.44

for a flight rangeequal to3000 [nmi] theaircraftweight is the𝑀𝑇𝑂𝑊. The remaining flightrangesarecomputeusinglinearinterpolationfromtheminimumflightrangetothemaximumflight range. The AEDT input file uses 6 profile steps which represent the takeoff weightassumingthemissionrangesare0–449[nmi],450–999[nmi] ,1000–1499[nmi] ,1500–2499[nmi],2500–3499[nmi],3500–999[nmi].Forthisstudy,sincethe20flighttrajectoriesarebetween500[nmi]and2200[nmi]theapplicableprofilesare2,3,and4.Therefore,theirrespectiveinterpolationsaresettocapturetheirmaximumweightintheprofilestep.

55

TASOpt

AEDT TASOpt𝑊! 𝐀 2 + 40,500+ (𝚨 1 − 𝚨 3 ∙ 0.85)/10

𝑊!,! 0–449[nmi] 𝐀 5 + 𝐀 2 at0[nmi]𝑊!,! 450–999[nmi] Interpolationusing999[nmi]𝑊!,! 1000–1499[nmi] Interpolationusing1499[nmi]𝑊!,! 1500–2499[nmi] Interpolationusing2100[nmi]𝑊!,! 2500–3499[nmi] 𝐀 1 at3000[nmi]𝑊!,! 3500–4499[nmi] Interpolationusing4499[nmi]

FLT_AIRFRAMES

AEDT:

UPDATE[FLEET].[dbo].[FLT_AIRFRAMES]SET[ENGINE_COUNT]=𝒏𝒆𝒏𝒈WHERE[AIRFRAME_ID]=1001

FLT_REF_ICAO_ACTYPES

AEDT:

UPDATE[FLEET].[dbo].[FLT_REF_ICAO_ACTYPES]SET[ENGINE_COUNT]=𝒏𝒆𝒏𝒈WHERE[ICAO_ACTYPE]='ZZ001'

56

ValidationThe validation study compares the fuel burn between an aircraft in TASOpt and the sameaircraftimportedandflowninAEDToverthethreeflightscenariosshowninError!Referencesourcenotfound..TheflightscenariosaregreatcircleflightsfromBostontoAtlanta,BostontoDenver,andBostontoLosAngeles.

Figure13:ValidationtrajectoryforTASOpt&AEDT

TogeneratetheAEDTsensorpaththeTASOptmoduleflewatotalof7missionswitheachofthethreeaircraftconfiguration.Thefirstmissionsizestheaircrafttotheoptimalconfiguration,whiletheevenandoddmissionsflewwithdifferentairportaltitudes.Forexample,missions2and 3 in TASOpt flew Boston to Atlanta using the departure airport altitude (mission 2) andarrivalairportaltitude(mission3).Thiswaywecouldgeneratetheflighttrajectory(e.g.,Bostonto Atlanta) by splitting the TASOpt output in midflight therefore having the correct airportdeparturealtitude(e.g.,Bostonmission2)andcorrectarrivalaltitude(e.g.,Atlantamission3).Theflighttrajectorydata(e.g.,latitude,longitude,altitude,andtrueairspeed)showninError!Reference sourcenot found. isused togenerate sensorpathandpopulate theASIFand theprocedurediscussedintheprevioussectionisusedtogenerateanAEDTversionoftheaircraft.

Error!Referencesourcenotfound.comparesthefuelburnandnetcorrectedthrustbetweentheTASOptandAEDTmodulesfortheBostontoAtlantaflight.Theresultsshowthefuelburnandnet corrected thrustmatchwell between the twomodules indicating themapping fromTASOpttoAEDTwassuccessful.Thearrivaldiscrepancyisduetothedifferencebetweenhow

57

AEDT 2a and TASOpt pull out of the cruise segment. AEDT 2s assumes the aircraft is idlewhereasTASOptdoesnot.

Figure14:D8withstandardtechnologyBOS-ATLflightsensorpathaltitudeandtrueairspeed.

58

Figure15:D8withstandardtechnologyAEDTvsTASOptBOS-ATLFuelBurnandNetCorrectThrustResults.

The total fuel burnassociated to a given flight segment is given inTable 17.The relativepercentuncertainty isgiven inError!Referencesourcenot found..Theresultsshowagood comparison betweenTASOpt andAEDT for the flight segments above 1,000 ft.Wenowdiscuss thediscrepanciesandpossiblesourcesofdifferencesbetweenmodules.TheflightfromBostontoDenverperformedworsethentheothertwoflightsduetotheflightpathsrange.TheBostontoDenverflightrangeis1520[nmi]whichisinthelowerrangeoftheAEDTstandardprofile3(i.e.,1500–2499[nmi]).TheAEDTstandardprofile3takeoffweightwasset to theTASOpt takeoffweightat2499 [nmi].Asa result, theAEDTusesatakeoffweightwhich is significantly larger than theTASOpt takeoffweight resulting inalargerfuelburnbyAEDT.TheAtlantaandLosAnglesflightshadrangesof850[nmi]and2300 [nmi] respectivelywhichput theAEDT takeoffweight closer to theTASOpt takeoffweight.Thisresultedinafaireragreementbetweenthemodulesfuelburns.Further,AEDTassumes theaircraft is carrying65% loadcapacitywhichwhenaccounted for inTASOptresulted in significant improvements between the modules results. Also, the flightsegmentswhich TASOpt and AEDT flew are slightly different (i.e.., +/- 1000 [ft]) due toAEDTsmodificationoftheflightpathscontainedintheASIF.Finally,weawarethatthereexists anunknown sourceof uncertaintywhich results in a7%shift betweenAEDTandTASOpt-AEDTtotalfuelburn.

59

Table17:(DataNotFinal)TotalfuelburncomparisonbetweenTASOptandAEDToverthreeflightscenariosandfiveflightsegments.

SegmentAltitude[ft]

TASOptBOS-ATL

AEDTBOS-ATL

TASOptBOS-DEN

AEDTBOS-DEN

TASOptBOS-LAX

AEDTBOS-LAX

Depart ≤ 1000 40.6 62.9 42.5 77.7 45.5 77.7Depart ≤ 10000 298.9 314.5 310.9 328.3 324.6 328.7 Cruise ≥ 10000 2389.7 2315.3 4317.5 4441.8 6449.9 6422.6Arrival≤ 10000 96.1 114.2 82.2 98.8 98.9 115.6Arrival ≤ 1000 9.3 24.9 8.2 15.8 9.5 25.7

𝑇𝑜𝑡𝑎𝑙 2784.7 2744.0 4710.6 4868.9 6873.4 6866.9

Table18:TASOptandAEDTcomparison;totalfuelburnandrelativepercentuncertainty.

BOS-ATL BOS-DEN BOS-LAX Total

Fuel[lb]%Difference Total

Fuel[lb]%Difference Total

Fuel[lb]%Difference

TASOpt 5015.6 - 8715.3 - 13186.4 -AEDT 4885.1 -2.60% 9014.5 2.37% 12524.3 -5.02%TASOpt-AEDT 5284.7 5.37% 9737.4 9.62% 13594.4 3.09%

Section5

System-LevelMCSUncertaintyQuantification

Theuncertaintyquantificationresultsinvestigatethefuelenergyconsumptionperpayloadrange(PFEI)givenas,

𝐹 = 𝑊!"#$!ℎ!"#$!!

𝑊!"#!𝑅!"!#$!!, Eq.45

where𝑊!"#$! is thetotal fuelburn,ℎ!"#$! is thefuelspecificheatvalue,𝑊!"#! is theaircraft

payloadweight,𝑅!"!#$! istheflightrange,and𝑘isthemissionnumber.Thefuelspecificheatvalueforthisanalysisisconsidereddeterministicandequaltothefuelspecificheatvalue

60

ofKerosene,46.0MJ/kg.Thepayloadweight isassumedtobetheaircraft takeoffweightminus theaircraftemptyweightand fuelburnweight.Thesummation inEq.45 is takenoverthe20flightscenariosdiscussedinSection4.

The uncertainty analysis is performedusing 10,000Monte Carlo simulations. The globalsensitivityanalysis isperformedusing1,000MonteCarlosimulations foreach individualinput.Theresultswillexamine thedistributionofPFEIand thesensitivityofPFEI to thesysteminputsforallthreeaircraftconfigurations.

B738StandardTechnologyTheuncertainty analysis result for theB738 is shown inFigure16.The expectation andstandarddeviationofPFEIare3.12kJ/kg/kmand0.064kJ/kg/kmrespectively.Theglobalsensitivity analysis results are shown in Figure 17. The sensitivity analysis indicates theimportant factors are cruise altitude and wing cap yield stress followed by operatingpressure ratio, gas temperature at turbine inlet in cruise conditions, and metaltemperature. The Monte Carlo simulation results for PFEI plotted against the aircrafttechnologyparametersareshowninFigure18.

61

Figure16:B738totalfuelenergyperpayloadrangedistribution.

Figure17:B738fuelenergyperpayloadrangesensitivityindex.

62

Figure18:B738MCSresultsofPFEIagainsttheaircrafttechnologyparameters.

TheresultsshowthatB738aircraftconfigurationPFEIissensitivetothecruisedesignaltitude.That is, uncertainty in theoperationof theB738 fleetwill haveadetrimental impactonourpredictabilityofaviationenvironmental impacts.Thesecond largest impact factor is thewingcapyieldstresswhichhasadirectimpactonthewingstructuralperformanceshowninFigure19.Thereasoncruisealtitudeandwingcapyieldstressuncertaintiesare importantfactors inthe uncertainty of PFEI is because they are also significant factors in the Boeing 737-800aircraft’semptyweightas shown inFigure20.Uncertainty in theaircraft’semptyweightwillhaveasignificant impactontheaircraft’sPFEIsinceit increasesuncertaintyassociatedtotheamountofpayloadtheaircraftmaycarryaboard.

63

The turbine inlet gas temperature, metal temperature, and operational pressure ratio aresignificantcontributorstouncertaintyinnominaltotalrateoffuelflowandmaximumtotalnetthrustasshowninFigure21.

Figure19:WingorTailSection(Drela,SimultaneousOptimizationoftheAirframe,Powerplant,andOperationofTransportAircraft.,2010)

Figure20:B738AircraftEmptyWeightSensitivityAnalysis.

Figure21:GlobalsensitivityindexforTC1andCf1

64

D8StandardTechnologyThe uncertainty analysis result for the D8 standard technology is shown in Figure 22. TheexpectationandstandarddeviationofPFEIare1.81kJ/kg/kmand0.033kJ/kg/kmrespectively.TheglobalsensitivityanalysisresultsareshowninFigure23.Thesensitivityanalysis indicatestheimportantfactorsarecruiseMachnumber,turbineinlettemperatureatcruiseconditions,turbineinlettemperatureattakeoffconditions,metaltemperature,wingcapsyieldstress,andcruise altitude. The Monte Carlo simulation results for PFEI plotted against the aircrafttechnologyparametersareshown inFigure24.TheD8standardtechnologyPFEIhasa lowervariancethantheB738standardtechnologyPFEI,whichindicatestheD8aircraftconfigurationpotentially, improves our ability to quantify PFEI. However, the drawback is that the D8standardtechnologyimportantfactorsarespreadacrossmultipleinputuncertainties.

Figure22:D8StandardTechnologyPFEIdistribution.

Figure23:D8StandardTechnologyPFEIsensitivityanalysis.

65

Figure24:D8StandardTechnologyMCSresultsofPFEIagainsttheaircrafttechnologyparameters.

TheD8standardtechnologyaircraftPFEIismoresensitivetotheuncertaintyintheaircraftengines technologywhereas the B738 PFEI ismore sensitive to uncertainty in both theaircraft’s technology and its operations. The D8 standard technology aircraft’s emptyweight sensitivity indiceshave contributions from the turbine inlet gas temperature andmetaltemperatureshowninFigure25.Theseengineparametersalsoplayasignificantroleintheaircraft’sfuelburnrateandthrustsensitivitiesshowninFigure26.Finally,theMachnumberhasthebiggestcontributingfactortotheD8standardtechnologyinduceddragandparasiticdragsensitivitiesshowninFigure27.

66

Figure25:D8StandardTechnologyAircraftEmptyWeightSensitivityAnalysis.

Figure26:D8StandardTechnologyGlobalsensitivityindexforCTC,1andCf1

Figure27:D8StandardTechnologyGlobalsensitivityindexforC0,CRandC2,CR

67

D8AdvancedTechnologyThe uncertainty analysis result for the D8 advanced technology is shown in Figure 28. TheexpectationandstandarddeviationofPFEIare1.10kJ/kg/kmand0.015kJ/kg/kmrespectively.Theglobal sensitivity analysis results are shown in Figure29Figure 23. The sensitivity analysisindicatestheimportantfactorsarecruiseMachnumberandturbineinlettemperatureatcruiseconditions.TheMonteCarlosimulationresultsforPFEIplottedagainsttheaircrafttechnologyparameters are shown in Figure 30. The D8 PFEI with advanced technologies shows animproved ability to quantify the aircraft’s PFEI (with lower variability). The D8 advancedtechnologyhasonlytwosignificantcontributingfactorstoPFEIvariance,comparedtotheD8standardtechnologywhichhadsixcontributingfactors.

Figure28:D8AdvancedTechnologyPFEIdistribution.

Figure29:D8AdvancedTechnologyPFEIsensitivityanalysis.

68

Figure30:D8AdvancedtechnologyMCSresultsofPFEIagainsttheaircrafttechnologyparameters.

The turbine inlet gas temperature at cruise conditions is a large contributing factor to theaircraft’snetthrustasshowninFigure31.TheMachnumberisasignificantcontributingfactortotheaircraft’sinducedandparasiticdragasshowninFigure32.TheD8advancedtechnologyhas high sensitivity to turbine inlet gas temperature at cruise conditions, which may berelativelysimplertoresearchandcontrolthanthecombineduncertaintiesofthesiximportantfactorsfortheD8standardtechnologyaircraft.

69

Figure31:D8advancedtechnologyGlobalsensitivityindexforCTC,1andCf1

Figure32:D8advancedtechnologyGlobalsensitivityindexforC0,CRandC2,CR

70

Section6

Decomposition-BasedUncertaintyQuantification

Decomposition-baseduncertainty quantificationperforms theuncertainty analysis and globalsensitivity analysis using a divide-and-conquer methodology motivated by multidisciplinarydesign and optimization algorithm architectures. Decomposing the uncertainty quantificationprocess provides a variety of benefits which include performing the UQ on themanageablecomponents,usinglocalresources,andbyexpertsinthespecificfield.Theuncertaintyanalysisresults are presented in this report and the global sensitivity analysis results are still underinvestigation.

TASOpt-AEDTInterfaceChallengeThechallengewiththedecomposition-baseduncertaintyanalysisapproachisinmanagingtheinterfaces between components. This challenge is exacerbated if the information beingtransferredbetweencomponentsishighdimensional(e.g.,>10).Inthisreport,theinformationtransferred between TASOpt and AEDT is on the O(100) variablesmaking this problem verychallenging. Furthermore, the O(100) variables are highly dependent which adds to thedifficultyofcharacterizingtheunderlyingprobabilitydistribution.Becauseofthedependenciesamong these variables, the global sensitivity analysis of the AEDT module would requireadvancedmethodswhichareunderdevelopmentandbeyondthescopeofthiswork.

Herewewillpresentabestpracticesfordecomposition-baseduncertaintyquantificationwhenthe information being transferred between components is high dimensional. Ourrecommended approach is to reduce the dimensions to the important variables, selecting agoodproposaldistribution,andperformingtheglobalcompatibilitysatisfactionstepefficiently.

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DimensionReductionThechallengingaspectoftheTASOpt-AEDTinterfaceisthenumberofinterfacevariables(i.e.,O(100))andthehighdependencyamongvariables.Theobjectivehereistoreducethenumberofinterfacevariablestoamoderatesizewhichstillcontainsallthenecessaryinformation.Thismeans the reduced set should contain the input variables to AEDT which are of greatestimportancetotheoutputofinterestvariance.Thesevariablescanbeidentifiedbythelargesttotal sensitivity indices based on a global sensitivity analysis. However, global sensitivityanalysis assumes the inputs are independent. Therefore, we will make two significantassumptionsinthiswork.Thefirstassumptionisthatvariableswiththelargesttotalsensitivityindicesintheindependentspacearealsothesamevariablesinthedependentspacewiththelargestimpactontheoutputofinterestvariance.Thesecondassumptionisthatthenumberofimportantvariablesaremoderate (i.e.,O(10)).Thisassumption isnecessarysincewewilluseQuasi-Monte Carlo simulation to evaluate the integrals required by the global sensitivityanalysis.Wenowfocusonhowtoselecttheimportancevariables.

JansenWindingStairsTheJansenwindingstairsmethodisasensitivityanalysisapproachbasedonscreeningmethodswhich were developed for large scale applications. A screening method is a qualitativesensitivity analysis approach while a variance based method is considered a quantitativesensitivityanalysisapproach.TheJansenwindingstairsmethodsamplesthehighdimensionalspace by modifying one dimension at a time. This is illustrated in Figure 33 for a threedimensionalproblem.Forourproblem,wecoupledthisapproachwithengineeringjudgmentinorder to select 17 important variables of the O(100) interface variables. The 17 importantvariablesarelistedinTable19.

Figure33:Jansenwindingstairssamplingmethod.

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Table19:The17importantinterfacevariablesselectedfromtheO(100)variables.

Variable DescriptionCtC1 ThrustCoefficient1MTOW MaximumTOWeightCtC3 ThrustCoefficient1CtC2 ThrustCoefficient1Cd2CR ParasiticDragCd0CR InducedDragS WingArea

Hmax MaximumAltitudeWmt AircraftEmptyWeightCf1 FuelCoefficient1VstCR CruiseStallVelocityCf2 FuelCoefficient2Cf3 FuelCoefficient3CfCR FuelCoef.CruiseHiCR_1 HiCruiseCAS1HiCR_2 HiCruiseCAS2HiCR_M HiCruiseMach

ProposalDistributionThe decomposition-based uncertainty analysis approach relies heavily on selecting a goodproposaldistribution.Aproposaldistribution is adistributionwe select toperform theAEDTuncertaintyanalysis.UponreceivingthetargetdistributionfromTASOpt,weadjusttheresultsfromtheproposaluncertaintyanalysistoestimatethetargetuncertaintyanalysis.However,toaccomplish this task we require that the proposal distribution encompasses the targetdistribution.Asanexample,inaonedimensionscenario,ifthetargetdistributionisU[0,1]thenanadequateproposalcouldbeU[-0.5,1.5].However,aninadequateproposalwouldbeU[0.5,2.5].Here theproblemof selectingangoodproposaldistribution is challenging sincewearedealing with an O(100) dimensional distribution. To accomplish this task we recommendperformingasmalluncertaintyanalysis(e.g.,1000samples)ofthesystem-levelMCStoobtainan estimate of the mean and variance of the interface distributions. We then increase thevariancetoencapsulate thenonobservable targetdistribution.Nextweuse forourproposaldistribution a multivariate Gaussian with the estimated mean and enlarged variance. ThisapproachcoupledwithexpertopinionwouldassistinselectingadequateproposaldistributionsasillustratedinFigure34.

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Figure34:Exampleselectionofanadequateproposaldistribution(WORKINPROGRES:IncreaseFontSize).

Proposal-to-TargetTransformationThefinalchallengerequirestransformingtheproposaldistributionintothetargetdistributionin order to estimate the module statistics under the target distribution. This step isencompassed in theglobal compatibility satisfaction step. Themethod requiresadjusting theweights associated to the proposal samples such that the statistics approximate the targetdistribution. The typical approach to computing these weights requires density estimationwhichdoes not scalewellwith dimensions. Insteadwehave formulated this problemas anoptimizationproblemthatoperatesdirectlyonthesamples;theoptimizationproblemhaslotsofstructuresowecanhandlelargescale(i.e.,largenumberofproposalsamples)applications.The proposed method to computing the importance weight minimizes the L2–norm, withrespect to the importanceweights,between theproposalempiricaldistribution functionandthetargetempiricaldistributionfunctionasshowninFigure35.

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Figure35:Proposedapproachtotransformtheproposaldistribution(U[0,1])intothetargetdistribution(Beta(0.5,0.5))adjuststheproposalsamplessuchthattheweightproposaldistribution(L2Oweighted)matchesthetargetdistribution.

UncertaintyAnalysisHere we only consider the Boeing 737-800 decomposition-based uncertainty analysis. Theapproach,asdescribedpreviously,reliesonpreformingtheuncertaintyanalysisofeachmoduleconcurrently.TheproposaldistributionfortheAEDTmoduleisselectedbasedonthepreviousdiscussion using 1,000 samples randomly selected from the system-level MCS uncertaintyanalysis.TheTASOptproposaldistributionisthesystem-levelMCSuncertaintyanalysis;thatistosayit isthetargetdistribution.Uponcompletingbothlocaluncertaintyanalysestheglobalcompatibility satisfaction step is performed. However, instead of using all O(100) interfacevariablesweuse the17 importantvariables inTable19.Theprocedureuses theoptimizationalgorithm shown in Figure 35 on the 17 dimensional distributions (e.g., see Figure 34 as anexample of 10 dimensions). The result is the AEDT modules output which was originallydistributedwith respect to the proposal distribution now is adjusted to represent the targetdistribution. This is illustrated in Figure 36. These results show that our decomposition-baseduncertaintyanalysisresultsvisuallymatchesthesystem-levelMCSresults.

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Figure36:Totalfuelburnusingthedecomposition-baseduncertaintyanalysismethodontheBoeing737-800.

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Section7

Conclusion

Quantifying an aircraft’s fuel burn performance is important for aviation policy analyses.However, our lack of knowledge in aircraft technologies and design operations result in anuncertain aircraft fuel burn performance, which must be quantified through an uncertaintyanalysis. This report studied the impact on aircraft fuel burn performance of varying aircraftconfigurationsandaviationtechnologicalenhancements.Theaircraft’sfuelburnperformancemethodology is based on a system-level tool composed of a conceptual-level aircraftperformance tool and an aviation environmental consequence tool. The uncertaintyquantification methodology is based on an all-at-once system-level approach and a newdecomposition-basedapproach.

Thesystem-level integrationcoupledaconceptual levelaircraftperformancetool,TASOpt, tothe aviation environmental design tool, AEDT 2a. The coupling of these two tools requiredpropagating approximately one hundred variables from the TASOpt module to the AEDTmodule.Theresultsofthiscouplingshowedgoodagreementoversimilarflightscenarioswithrespecttofuelburnfortheclimbabove10,000[ft]andcruisesegment.Withtheseresults,wehave drawn comparisons between TASOpt and AEDT fuel burn calculations which can drivesoftwaredeveloperstoinvestigateandimproveupontheirrespectivetools.Thestudyrevealedadrawback,ofwhichtheAEDTdevelopersareaware,inAEDT’scalculationoffuelburnduringthedescentoutofcruise. In thedescentoutofcruisesegment,AEDTassumestheaircraft isdescendingwith the engines idling,which is not a typical flight procedure. The analysis alsorevealedthatitispossibletoincuratworstcasefuelburnabsoluteerrorofapproximately3.0%in assuming a step change in takeoff aircraft weight versus range instead of a continuouschangeintakeoffaircraftweightversusrange.Finally,thefuelburnintheAEDTclimbsegmentdoes not seem realistic and the author attributes this discrepancy to possible interpolationeffectsinAEDT.

The system-level uncertainty quantification offered multiple insights into the impacts ofuncertaintyinaircrafttechnologiesanddesignoperationsonquantifyinganaircraft’sfuelburnperformance. The Boeing 737-800 uncertainty quantification revealed that the conventional

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aircraft configuration incurs a significant variation in PFEI which can be attributed touncertainties in design cruise altitude and wing cap yield stress. The lack of knowledge fordesign cruise altitude andwing cap yield stress have a significant impact on the uncertaintyassociatedtotheaircraftemptyweightwhichinturndirectlyimpactstheaircraft’sPFEI.TheD8with standard technology aircraft configuration had approximately half the variation in PFEIthan the Boeing 737-800. The drawback with the D8 standard technology is that the PFEIuncertainty is attributed tomultiple aircraft technologies and design operations uncertainty.Thismakesitdifficulttodeterminewhichfactortoprioritizeforfutureresearchendeavors.TheD8with advanced technology had approximately half the variation in PFEI than theD8withstandard technology. Also, the uncertainty in PFEI is mainly attributed to a single aircrafttechnology, turbine inletgas temperatureatcruiseconditions,andasingledesignoperation,cruiseMachnumber.

Theseresultshaveofferedameaningfulconclusion:uncertaintyinPFEIisdependentonaircraftconfigurations and aviation technological enhancements. Furthermore, uncertainty in PFEIacrossvaryingaircraft configurationsandaviation technologicalenhancements is significantlyaffectedbydifferentaircrafttechnologiesanddesignoperations.

The report also investigated the implementation of our decomposition-based uncertaintyquantification method on a large-scale application problem. The results show ourdecomposition-baseduncertainty analysis approach coupledwith thebestpracticesmatchedthe system-level MCS results. We have provided evidence that even in high dimensionalinterfacesourmethodcanstillbeappliedassumingtheinformationbeingtransferredlivesinalowdimensionalsubspace.Wehavealsodemonstratedthatouroptimizationbasedapproachtothetransportofdistributionsproblemworksinrelativelylargedimensions.However,futureresearchisrequiredtoimproveourdecomposition-baseduncertaintyquantificationapproach.A method which systematically identifies the variables of importance when the inputdistributionsaredependentwouldassistourmethodbyreducingtheinterfacedimensions.

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References2010a,I.(2010).Reportofthecommitteeonaviationenviornmentalprotection,Eighth

Meeting.Montreal,1-12:Doc9938CAEP/8.

2010b,I.(2010).37thSessionoftheICAOAssembly,ResolutionA37-19:ConsolidatedstatementofcontinuingICAOpoliciesandpracticesrelatedtoenviornmentalprotectionclimatechange.

Administration,F.A.(2013).AviationEnviornmentalDesignTool(AEDT)2aUncertiantyQuantificationReport.U.S.DepartmentofTransportation.

Allaire,D.(2009).UncertaintyAssessmentofComplexModelswithApplicationtoAviationEnvironmentalSystems.MassachusettsInstituteofTechnology.

Amaral,S.,Allaire,D.,&Willcox,K.(2012).ADecompositionApproachtoUncertaintyAnalysisofMultidisciplinarySystems.12thAIAAAviationTechnology,Integration,andOperations(ATIO)Conferenceand14thAIAA/ISSM,(pp.1-18).Indianapolis,Indiana.

AndreaSaltelli,M.R.(2008).Globalsensitivityanalysis:theprimer.Wiley.

BADA.(2012).UserManualfortheBaseofAircraftData(BADA)Revision3.10.EECTechnical/ScientificReportNo.12/04/10-45.

Cumpsty,N.,Alonso,J.,Eury,S.,Maurice,L.,Nas,B.,Ralph,M.,&Sawyer,R.(2010).ReportoftheIndependentExpertsonFuelBurnReductionTechnology.CAEP-SG/20101-WP/11Doc9963.

Dons,J.,Mariens,J.,&O'Callaghan,G.(2011).UseofThird-partyAircraftPerformanceToolsintheDevelopmentoftheAviationEnviornmentalDesignTool(AEDT).DOT-VNTSC-FAA-11-08.

Drela,M.(2010).DevelopmentoftheD8TransportConfiguration.AIAATransportAircraft.

Drela,M.(2010).SimultaneousOptimizationoftheAirframe,Powerplant,andOperationofTransportAircraft.HamiltonPlace.

Greitzer,E.,Bonnefoy,P.,Blanco,E.d.,Dorbian,C.,Drela,M.,Hall,D.,...et,a.(2010).N+3AircraftConceptDesignsandTradeStudies.NASA/CR-2010-216794/Vol2.

Gunston,B.(1998).Jane'sAero-Engines.Jane'sInformationGroup.

Kyprianidis,K.(2011).FutureAeroEngineDesigns:AnEvolvingVision.

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Lee,D.,Fahey,D.,Forster,P.M.,Newton,P.J.,Wit,R.C.,Lim,L.L.,...Sausen,R.(2009).Aviationandglobalclimatechangeinthe21stcentury.AtmosphericEnviornment43no.22,3520-3537.

Manual,A.T.(2012).AviationEnviornmentalDesignTool(AEDT)2a:TechnicalManual.DOT-VNTSC-FAA-12-09.

Niederreiter,H.(1992).RandomNumberGenerationandQuasi-MonteCarloMethods.SocietyforIndustrialandAppliedMathematics.

Roof,C.,Hansen,A.,Fleming,G.,Thrasher,T.,Nguyen,A.,Hall,C.,...Hollingsworth,P.(2007).Aviationenvironmentaldesigntool(AEDT)systemarchitecture.Doc#AEDT-AD-01.

Rutherford,D.,&Mazyar,Z.(2009).Efficiencytrendsfornewcommericaljetaircraft1960to2008.InternationalCouncilonCleanTransportation.

AppendixA

GlobalSensitivityAnalysisToperformGSA,theSobol’methodwhichutilizestheMonte-CarloSimulationsisapplied.ThealgorithmtosolvetheGSAanalysisisshownbelow.[Saltelli(2008)]

A = Input Vector =

X!! X!

(!) ⋯X!! X!

(!) ⋯⋯ ⋯ ⋯

X!! ⋯ X!

(!)

X!! ⋯ X!

(!)

⋯ ⋯ ⋯X!! X!

(!) ⋯ X!(!) ⋯ X!

(!)

A = Input Vector =

X!!!! X!!!

(!) ⋯

X!!!! X!!!

(!) ⋯⋯ ⋯ ⋯

X!!!! ⋯ X!!!

(!)

X!!!! ⋯ X!!!

(!)

⋯ ⋯ ⋯X!!!! X!!!

(!) ⋯ X!!!(!) ⋯ X!!!

(!)

80

A = Input Vector =

X!!!! X!!!

(!) ⋯

X!!!! X!!!

(!) ⋯⋯ ⋯ ⋯

X!! ⋯ X!!!

(!)

X!! ⋯ X!!!

(!)

⋯ ⋯ ⋯X!!!! X!!!

(!) ⋯ X!(!) ⋯ X!!!

(!)

𝑀𝑜𝑑𝑢𝑙𝑒 𝑥 = 𝑓 𝑥 : 𝑦! = 𝑓 𝐴 , 𝑦! = 𝑓 𝐵 , 𝑦! = 𝑓 𝐶

𝑓! =1𝑁 𝑦!

!!!!! + 1

𝑁 𝑦!!!

!!!

2

𝑦! = 𝑦! − 𝑓! ,𝑦! = 𝑦! − 𝑓!,𝑦! = 𝑦! − 𝑓!

𝑉 𝑌 = 𝑦! ∙ 𝑦! − 𝑓!! = 1𝑁 𝑦!

! ∙ 𝑦!!

!

!!!

− 𝑓!!

𝑆! = 𝑀𝑎𝑖𝑛 𝐸𝑓𝑓𝑒𝑐𝑡 =𝑉 𝐸 𝑌|𝑋!𝑉 𝑌 =

𝑦! ∙ 𝑦!! − 𝑓!!

𝑦! ∙ 𝑦! − 𝑓!!=1𝑁 𝑦!

! ∙ 𝑦!!!!

!!! − 𝑓!!

1𝑁 𝑦!

! ∙ 𝑦!!!

!!! − 𝑓!!

𝑆!" = 𝑇𝑜𝑡𝑎𝑙 𝐸𝑓𝑓𝑒𝑐𝑡 = 1−𝑉 𝐸 𝑌|𝑋~!

𝑉 𝑌 = 1−𝑦! ∙ 𝑦!! − 𝑓!

!

𝑦! ∙ 𝑦! − 𝑓!!=1𝑁 𝑦!

! ∙ 𝑦!!!!

!!! − 𝑓!!

1𝑁 𝑦!

! ∙ 𝑦!!!

!!! − 𝑓!!

AppendixB

TASOptInputFiles(*.tas)

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AppendixC

AEDTSQLFleetDatabaseImport(*.sql) Insert Into [FLEET].[dbo].[FLT_REF_ICAO_ACTYPES] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited (,);"','select * from FLT_REF_ICAO_ACTYPES.csv') Insert Into [FLEET].[dbo].[FLT_ACTYPES] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_ACTYPES.csv') SET IDENTITY_INSERT FLEET.dbo.FLT_AIRFRAMES ON Insert Into [FLEET].[dbo].[FLT_AIRFRAMES] ([AIRFRAME_ID] ,[MODEL],[ENGINE_COUNT],[ENGINE_LOCATION],[DESIGNATION_CODE] ,[EURO_GROUP_CODE],[MAX_RANGE],[INTRO_YEAR],[USAGE_CODE] ,[SIZE_CODE],[ENGINE_TYPE]) select [AIRFRAME_ID],[MODEL],[ENGINE_COUNT],[ENGINE_LOCATION] ,[DESIGNATION_CODE],[EURO_GROUP_CODE],[MAX_RANGE],[INTRO_YEAR] ,[USAGE_CODE],[SIZE_CODE] ,[ENGINE_TYPE] from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_AIRFRAMES.csv') SET IDENTITY_INSERT FLEET.dbo.FLT_AIRFRAMES OFF Insert Into [FLEET].[dbo].[FLT_REF_ACCODES] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_REF_ACCODES.csv') Insert Into [FLEET].[dbo].[FLT_AIRFRAME_ACTYPE_MAP] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_AIRFRAME_ACTYPE_MAP.csv') Insert Into [FLEET].[dbo].[FLT_BADA_ACFT]

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select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_BADA_ACFT.csv') Insert Into [FLEET].[dbo].[FLT_ANP_AIRPLANES] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_ANP_AIRPLANES.csv') SET IDENTITY_INSERT [FLEET].[dbo].[FLT_EQUIPMENT] ON Insert Into [FLEET].[dbo].[FLT_EQUIPMENT] ([EQUIP_ID] ,[AIRFRAME_ID],[ENGINE_ID],[ENGINE_MOD_ID] ,[ANP_AIRPLANE_ID],[ANP_HELICOPTER_ID],[BADA_ID]) select [EQUIP_ID],[AIRFRAME_ID],[ENGINE_ID],[ENGINE_MOD_ID] ,[ANP_AIRPLANE_ID],[ANP_HELICOPTER_ID] ,[BADA_ID] from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_EQUIPMENT.csv') SET IDENTITY_INSERT [FLEET].[dbo].[FLT_EQUIPMENT] OFF SET IDENTITY_INSERT [FLEET].[dbo].[FLT_DEFAULT_ENGINES] ON Insert Into [FLEET].[dbo].[FLT_DEFAULT_ENGINES] ([DEF_ENG_ID] ,[ENG_ID],[AIRFRAME_ID],[REGION_CODE],[SOURCE]) select [DEF_ENG_ID],[ENG_ID],[AIRFRAME_ID],[REGION_CODE] ,[SOURCE] from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_DEFAULT_ENGINES.csv') SET IDENTITY_INSERT [FLEET].[dbo].[FLT_DEFAULT_ENGINES] OFF SET IDENTITY_INSERT [FLEET].[dbo].[FLT_FLEET] ON Insert Into [FLEET].[dbo].[FLT_FLEET] ([FLEET_ID] ,[AIRFRAME_ID],[ENGINE_ID],[ENGINE_MOD_ID],[DATE_START] ,[DATE_END],[REF_ACCODE],[REF_ENG_CODE],[REF_ENG_MOD_CODE]

,[EQGROUP],[SERIAL_NO],[REG_NO],[AC_TYPE_DESC],[ENG_TYPE],[WINGLETS],[HUSH_TYPE],[HUSH_TYPE_CODE],[COMBUSTOR],[ROLE],[DELDATE] ,[OPERATOR],[COUNTRY_CD],[MAX_TAKEOFF_WGT],[MAX_TAKEOFF_WGT_LK] ,[MAX_LANDING_WGT],[MAX_LANDING_WGT_LK],[CERT_NOISE_LEVEL_TAKEOFF]

,[CERT_NOISE_LEVEL_SIDELINE],[CERT_NOISE_LEVEL_APPROACH] ,[STG3_TRADE_MARGIN_CUM],[NOX_CHAR],[CAEP_4_NOX_MARGIN] ,[ENG_PRESSURE_RATIO],[ENG_MAX_RATED_THRUST],[SOURCE_TYPE] ,[SOURCE],[AEDT_SEATS],[AEDT_SEATS_SOURCE] ,[AEDT_OPERATING_EMPTY_WEIGHT_LBS] ,[AEDT_OPERATING_EMPTY_WEIGHT_LBS_SOURCE]

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,[AGE],[FESG_RETIREMENT_CURVE_ID],[OEW],[OEW_SOURCE],[MAX_PAYLOAD] ,[EQCAT],[OPERATOR_ICAO_DEPRECATED],[OPERATOR_IATA_DEPRECATED] ,[COUNTRY_LAR],[COUNTRY_OAG],[AEDT_CARRIER_CODE] ,[FUEL_CAPACITY_US_GALS_FLOAT] select ([FLEET_ID],[AIRFRAME_ID],[ENGINE_ID],[ENGINE_MOD_ID],[DATE_START] ,[DATE_END],[REF_ACCODE],[REF_ENG_CODE],[REF_ENG_MOD_CODE]

,[EQGROUP],[SERIAL_NO],[REG_NO],[AC_TYPE_DESC],[ENG_TYPE],[WINGLETS],[HUSH_TYPE],[HUSH_TYPE_CODE],[COMBUSTOR],[ROLE],[DELDATE] ,[OPERATOR],[COUNTRY_CD],[MAX_TAKEOFF_WGT],[MAX_TAKEOFF_WGT_LK] ,[MAX_LANDING_WGT],[MAX_LANDING_WGT_LK],[CERT_NOISE_LEVEL_TAKEOFF]

,[CERT_NOISE_LEVEL_SIDELINE],[CERT_NOISE_LEVEL_APPROACH] ,[STG3_TRADE_MARGIN_CUM],[NOX_CHAR],[CAEP_4_NOX_MARGIN] ,[ENG_PRESSURE_RATIO],[ENG_MAX_RATED_THRUST],[SOURCE_TYPE] ,[SOURCE],[AEDT_SEATS],[AEDT_SEATS_SOURCE] ,[AEDT_OPERATING_EMPTY_WEIGHT_LBS] ,[AEDT_OPERATING_EMPTY_WEIGHT_LBS_SOURCE] ,[AGE],[FESG_RETIREMENT_CURVE_ID],[OEW],[OEW_SOURCE],[MAX_PAYLOAD] ,[EQCAT],[OPERATOR_ICAO_DEPRECATED],[OPERATOR_IATA_DEPRECATED] ,[COUNTRY_LAR],[COUNTRY_OAG],[AEDT_CARRIER_CODE] ,[FUEL_CAPACITY_US_GALS_FLOAT] from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_FLEET.csv') SET IDENTITY_INSERT [FLEET].[dbo].[FLT_FLEET] OFF SET IDENTITY_INSERT [FLEET].[dbo].[FLT_DISPERSION] ON Insert Into [FLEET].[dbo].[FLT_DISPERSION] ([DISPERSION_ID] ,[REL_HEIGHT],[SIGMAZ0],[AIRFRAME_ID]) select [DISPERSION_ID],[REL_HEIGHT],[SIGMAZ0] ,[AIRFRAME_ID] from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_DISPERSION.csv') SET IDENTITY_INSERT [FLEET].[dbo].[FLT_DISPERSION] OFF Insert Into [FLEET].[dbo].[FLT_BADA_CONFIG] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_BADA_CONFIG.csv') Insert Into [FLEET].[dbo].[FLT_BADA_FUEL] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_BADA_FUEL.csv')

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Insert Into [FLEET].[dbo].[FLT_BADA_APF] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_BADA_APF.csv') Insert Into [FLEET].[dbo].[FLT_BADA_ALTITUDE_DISTRIBUTION] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_BADA_ALTITUDE_DISTRIBUTION.csv') Insert Into [FLEET].[dbo].[FLT_BADA_THRUST] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_BADA_THRUST.csv') Insert Into [FLEET].[dbo].[FLT_ANP_AIRPLANE_FLAPS] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_ANP_AIRPLANE_FLAPS.csv') SET IDENTITY_INSERT [FLEET].[dbo].[FLT_ANP_AIRPLANE_PROFILES] ON Insert Into [FLEET].[dbo].[FLT_ANP_AIRPLANE_PROFILES] ([ACFT_ID] ,[OP_TYPE],[PROF_ID1],[PROF_ID2],[PROFILE_ID],[WEIGHT]) select [ACFT_ID],[OP_TYPE],[PROF_ID1],[PROF_ID2],[PROFILE_ID] ,[WEIGHT] from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_ANP_AIRPLANE_PROFILES.csv') SET IDENTITY_INSERT [FLEET].[dbo].[FLT_ANP_AIRPLANE_PROFILES] OFF Insert Into [FLEET].[dbo].[FLT_ANP_AIRPLANE_PROCEDURES] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_ANP_AIRPLANE_PROCEDURES.csv') Insert Into [FLEET].[dbo].[FLT_ANP_AIRPLANE_PROCEDURES_EXT] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_ANP_AIRPLANE_PROCEDURES.csv')

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%%%%% NOT USED BY 737700 AIRCRAFT %%%%% Insert Into [FLEET].[dbo].[FLT_ANP_AIRPLANE_PROFILE_POINTS] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_ANP_AIRPLANE_PROFILE_POINTS.csv') Insert Into [FLEET].[dbo].[FLT_ANP_AIRPLANE_PROFILE_POINTS_EXT] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_ANP_AIRPLANE_PROFILE_POINTS.csv') %%%%% NOT USED BY 737700 AIRCRAFT %%%%% Insert Into [FLEET].[dbo].[FLT_ANP_AIRPLANE_THRUST_JET] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_ANP_AIRPLANE_THRUST_JET.csv') Insert Into [FLEET].[dbo].[FLT_ANP_AIRPLANE_TSFC_COEFFICIENTS] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_ANP_AIRPLANE_TSFC_COEFFICIENTS.csv') Insert Into [FLEET].[dbo].[FLT_ACTYPE_CARRIER] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_ACTYPE_CARRIER.csv') Insert Into [FLEET].[dbo].[FLT_REF_ANP_EQUIPMENT_DEFAULT] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_REF_ANP_EQUIPMENT_DEFAULT.csv') Insert Into [FLEET].[dbo].[FLT_ANP_BADA_ENERGYSHARE] select * from OpenRowset('MSDASQL', 'Driver={Microsoft Access Text Driver (*.txt, *.csv)}; DefaultDir=D:\TASOpt\AEDT_Aircraft\CSV\;Extended properties="ColNameHeader=True;Format=Delimited(,);"','select * from FLT_ANP_BADA_ENERGYSHARE.csv')

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AppendixD

SQLScripttoDuplicateOperations

Duplicate[AIR_OPERATION_AIRCRAFT]

SET IDENTITY_INSERT [TEST].[dbo].[AIR_OPERATION_AIRCRAFT] ON INSERT INTO [TEST].[dbo].[AIR_OPERATION_AIRCRAFT] ([AIRCRAFT_ID] ,[NAME],[EQUIPMENT_ID],[AIRCRAFT_SOURCE],[DESCRIPTION]) VALUES (2,'MIT1',5001,0,'MIT1') INSERT INTO [TEST].[dbo].[AIR_OPERATION_AIRCRAFT] ([AIRCRAFT_ID] ,[NAME],[EQUIPMENT_ID],[AIRCRAFT_SOURCE],[DESCRIPTION]) VALUES (3,'MIT2',5002,0,'MIT2') . . . INSERT INTO [TEST].[dbo].[AIR_OPERATION_AIRCRAFT] ([AIRCRAFT_ID] ,[NAME],[EQUIPMENT_ID],[AIRCRAFT_SOURCE],[DESCRIPTION]) VALUES (1000,'MIT999',5999,0,'MIT999') SET IDENTITY_INSERT [TEST].[dbo].[AIR_OPERATION_AIRCRAFT] OFF

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Duplicate[AIR_OPERATION]

INSERT INTO [TEST].[dbo].[AIR_OPERATION] ([AIRCRAFT_ID],[CASE_ID],[USER_ID],[OPERATION_TYPE],[OP_COUNT],[OPERATION_TIME],[DEPARTURE_AIRPORT_LAYOUT_ID],[DEPARTURE_RUNWAY_END_ID],[ARRIVAL_AIRPORT_LAYOUT_ID],[ARRIVAL_RUNWAY_END_ID],[SENSOR_PATH_ID]) SELECT 2,[CASE_ID],[USER_ID],[OPERATION_TYPE],[OP_COUNT],[OPERATION_TIME],[DEPARTURE_AIRPORT_LAYOUT_ID],[DEPARTURE_RUNWAY_END_ID],[ARRIVAL_AIRPORT_LAYOUT_ID],[ARRIVAL_RUNWAY_END_ID],[SENSOR_PATH_ID] from [TEST].[dbo].[AIR_OPERATION] WHERE [AIRCRAFT_ID] = 1 INSERT INTO [TEST].[dbo].[AIR_OPERATION] ([AIRCRAFT_ID],[CASE_ID],[USER_ID],[OPERATION_TYPE],[OP_COUNT],[OPERATION_TIME],[DEPARTURE_AIRPORT_LAYOUT_ID],[DEPARTURE_RUNWAY_END_ID],[ARRIVAL_AIRPORT_LAYOUT_ID],[ARRIVAL_RUNWAY_END_ID],[SENSOR_PATH_ID]) SELECT 3,[CASE_ID],[USER_ID],[OPERATION_TYPE],[OP_COUNT],[OPERATION_TIME],[DEPARTURE_AIRPORT_LAYOUT_ID],[DEPARTURE_RUNWAY_END_ID],[ARRIVAL_AIRPORT_LAYOUT_ID],[ARRIVAL_RUNWAY_END_ID],[SENSOR_PATH_ID] from [TEST].[dbo].[AIR_OPERATION] WHERE [AIRCRAFT_ID] = 1 . . . INSERT INTO [TEST].[dbo].[AIR_OPERATION] ([AIRCRAFT_ID],[CASE_ID],[USER_ID],[OPERATION_TYPE],[OP_COUNT],[OPERATION_TIME],[DEPARTURE_AIRPORT_LAYOUT_ID],[DEPARTURE_RUNWAY_END_ID],[ARRIVAL_AIRPORT_LAYOUT_ID],[ARRIVAL_RUNWAY_END_ID],[SENSOR_PATH_ID]) SELECT 1000,[CASE_ID],[USER_ID],[OPERATION_TYPE],[OP_COUNT],[OPERATION_TIME],[DEPARTURE_AIRPORT_LAYOUT_ID],[DEPARTURE_RUNWAY_END_ID],[ARRIVAL_AIRPORT_LAYOUT_ID],[ARRIVAL_RUNWAY_END_ID],[SENSOR_PATH_ID] from [TEST].[dbo].[AIR_OPERATION] WHERE [AIRCRAFT_ID] = 1

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